Math 251, Test 2 Wednesday, May 19, 2004
|
|
- Brook Price
- 5 years ago
- Views:
Transcription
1 Math 251, Test 2 Wednesday, May 19, 2004 Name: Hints and Answers Instructions. Complete each of the following 9 problems. Please show all appropriate details in your solutions. Good Luck. 1. (15 pts) (a) Find the mean and standard deviation for the sampling distribution for x based on a sample size of 81 from a population with mean 37 and standard deviation 6. Answer. µ x = 37 and σ x = 6 81 = 2 3. (b) Find z c when c =.96. Answer. Find z-value corresponding to an area of /2 =.98. Thus z (c) What z-value would you obtain for a data value that is 3 standard deviations below the mean? Answer. z = 3. (d) If a population has a standard deviation of 10, what sample size would be necessary in order for a 99% confidence interval to estimate the population mean within ±2? Answer. n = ( zc σ E ) ( ) = Thus we would use a sample size of n = (e) What size of random sample is needed by a polling organization to estimate a population percentage within plus or minus 1% with 95% confidence. In your calculation assume that there is no preliminary estimate for p. Answer. n = 1 4 ( ) = (f) What proportion of data in a normal population lies within 2.5 standard deviations of the mean? Answer. From the table, we find P ( 2.5 < z < 2.5) = = (g) Let x be the random variable that represents the weight of a randomly selected Gabon Viper. Is x a continuous or discrete random variable? Answer. x is a continuous random variable, because it can theoretically take any value larger than 0, i.e. it can be any value in an interval.
2 2. (a) (1 pt) Fill in the missing probability for the following discrete random variable. x P (x) (b) Find the mean and standard deviation of the random variable x with distribution as follows. x P (x) Answer. The mean is µ = xp (x) = 2(.35) + 3(.30) + 5(.15) = While σ 2 = 2 2 (.35) (.30) (.15) = Therefore, the standard deviation is σ = Suppose the probability Kobe Bryant will make a free throw is Suppose Mr. Bryant will have 14 free throw attempts in his next game. Find: (a) (2 pts) The probability that he will make all 14 free throws. Answer. P (r = 14) = = (b) (2 pts) The probability that he will make exactly 13 free throws. Answer. P (r = 13) = C 14,13 (.84) 13 (.16) 1 = 14(.84) 13 (.16) = (c) (1 pts) The probability that he will make 12 or fewer free throws. Answer. The answer is approximately 1 ( ) = =.6807.
3 4. Northwest Airlines has found that 96% of people with tickets will show up for their Friday afternoon flight from Detroit to Amsterdam. Suppose that there are 300 passengers holding tickets for this flight, and the jet can carry 294 passengers, and that the decisions of passengers to show up are independent of one another. (a) (1 pts) Verify that the normal approximation of the binomial distribution can be used for this problem. Answer. We check that np = (300)(.96) = 288 > 5 and nq = (300)(.04) = 12 > 5. (b) (4 pts) Use the normal approximation to the binomial distribution to find the probability that from 285 to 294 passengers (including 285 and 294) will show up for the flight. Answer. By (a), this binomial distribution is approximately normal, and it has mean µ = 288 and standard deviation σ = npq = (300)(.96)(.04) Using the continuity correction, we compute P (285 r 294) P (284.5 x 294.5) = P ( 1.03 z 1.915) = = Suppose the distribution of weights of adult female American Landrace pigs is normally distributed with a mean of 300 lbs and standard deviation of 40 lbs. (a) (2 pts) What weight is at the 20th percentile? Answer. The z-value corresponding to the 20th percentile is z =.84, thus the corresponding weight is x = (.84)(40) = lbs. (b) (2 pts) What proportion of adult female American Landrace pigs weigh between 230 lbs and 290 lbs? Answer. P (230 < x < 290) = P ( 1.75 < z <.25) = = (c) (1 pt) What proportion of adult female American Landrace pigs weigh more than 290 lbs? Answer. P (x > 290) = P (z >.25) = =.5987.
4 6. (5 pts) The encyclopedia of erroneous data reports that the mean weight of adult male polar bears is 1100 lbs. (a) Suppose a wildlife biologist collects a random sample of 64 adult male polar bears and finds that x = 1150 lbs and s = 130 lbs. If the true population mean is 1100 lbs, what is the probability of finding a sample mean of x = 1150 lbs or greater? Assume that σ = 130 lbs. Answer =.001. P ( x 1150) = P ( z ) = P (z 3.077) 1 P (z < 3.08) = (b) Based on the sample in (a), would you be skeptical of that the mean weight of adult male polar bears is 1100 lbs? Explain. Answer. Very skeptical. If the mean weight were 1100 lbs, there would only be.001 probability of obtaining the sample in (a), hence, assuming the biologists sample was random, and the statistics are correct, we are quite certain that the true mean weight is more than 1100 lbs. 7. (5 pts) In a recent poll of 1009 randomly selected adult Americans it was reported that 44% of adult Americans surveyed approve of the way the United States has handled the war in Iraq. (a) Find a 95% confidence interval for the proportion of adult Americans that approve of the way the United States has handled the war in Iraq. (.44)(.56) Answer. The confidence interval has endpoints.44 ± 1.96, and so the interval is 1009 (.4094,.4706). (b) Based on (a) would you be comfortable saying that less than 45% of all adult Americans approve of the way the United States has handled the war in Iraq? Explain. Answer. No, you should not be comfortable saying that because you are 95% sure that the true percentage of support is between 40.94% and 47.06%; which leaves a good portion of interval above 45%, indicating there is a reasonable chance that the true level of support is more than 45%.
5 8. (5 pts) A recent survey of 400 randomly selected gas stations in America found that the average price for unleaded gasoline is $2.02. That is, in their sample, they found x = $2.02 and s = $0.15. (a) Find a 99% confidence interval for the mean price of unleaded gasoline in America. Answer. The confidence interval has endpoints 2.02 ± Thus the 99% confidence interval is ( , ). (b) Based on your interval in (a), would you be comfortable saying that the mean price of unleaded gas in America is at least $2.00? Explain. Answer. Yes, I am 99% sure that the true mean price is between $2.00 and $2.04 which is at least $ (5 pts) In a random sample of 50 gas stations in California it was found that the sample mean price of unleaded gasoline was $2.21 with a standard deviation of $0.17. At the same time, a random sample of 60 gas stations in New York had a sample mean price of $2.17 for unleaded gasoline with a standard deviation of $0.16. (a) Find a 95% confidence interval for the difference in unleaded gasoline prices between California and New York. (.17) 2 Answer. The confidence interval has endpoints ( ) ± (.16) , so the endpoints are approximately.04 ± (1.96)( ). Hence the confidence interval is (.0221,.1021). (b) Interpret the interval in (a). Does it strongly suggest that gasoline prices in California are higher than in New York? Answer. We are 95% sure that the mean price of unleaded gasoline in California is from 2 cents lower to 10 cents higher than the mean price in New York. Hence there is still a reasonable possibility that the mean price in California is lower, therefore the interval in (a) does not strongly suggest that the mean price in California is higher.
Math 251: Practice Questions Hints and Answers. Review II. Questions from Chapters 4 6
Math 251: Practice Questions Hints and Answers Review II. Questions from Chapters 4 6 II.A Probability II.A.1. The following is from a sample of 500 bikers who attended the annual rally in Sturgis South
More informationNo, because np = 100(0.02) = 2. The value of np must be greater than or equal to 5 to use the normal approximation.
1) If n 100 and p 0.02 in a binomial experiment, does this satisfy the rule for a normal approximation? Why or why not? No, because np 100(0.02) 2. The value of np must be greater than or equal to 5 to
More informationAMS7: WEEK 4. CLASS 3
AMS7: WEEK 4. CLASS 3 Sampling distributions and estimators. Central Limit Theorem Normal Approximation to the Binomial Distribution Friday April 24th, 2015 Sampling distributions and estimators REMEMBER:
More informationFINAL REVIEW W/ANSWERS
FINAL REVIEW W/ANSWERS ( 03/15/08 - Sharon Coates) Concepts to review before answering the questions: A population consists of the entire group of people or objects of interest to an investigator, while
More informationEstimation. Focus Points 10/11/2011. Estimating p in the Binomial Distribution. Section 7.3
Estimation 7 Copyright Cengage Learning. All rights reserved. Section 7.3 Estimating p in the Binomial Distribution Copyright Cengage Learning. All rights reserved. Focus Points Compute the maximal length
More informationMA131 Lecture 9.1. = µ = 25 and σ X P ( 90 < X < 100 ) = = /// σ X
The Central Limit Theorem (CLT): As the sample size n increases, the shape of the distribution of the sample means taken with replacement from the population with mean µ and standard deviation σ will approach
More informationUniversity of California, Los Angeles Department of Statistics
University of California, Los Angeles Department of Statistics Statistics 13 Instructor: Nicolas Christou The central limit theorem The distribution of the sample proportion The distribution of the sample
More informationCH 5 Normal Probability Distributions Properties of the Normal Distribution
Properties of the Normal Distribution Example A friend that is always late. Let X represent the amount of minutes that pass from the moment you are suppose to meet your friend until the moment your friend
More informationSection 7.5 The Normal Distribution. Section 7.6 Application of the Normal Distribution
Section 7.6 Application of the Normal Distribution A random variable that may take on infinitely many values is called a continuous random variable. A continuous probability distribution is defined by
More informationKey Concept. 155S6.6_3 Normal as Approximation to Binomial. March 02, 2011
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal
More informationUniversity of California, Los Angeles Department of Statistics. The central limit theorem The distribution of the sample mean
University of California, Los Angeles Department of Statistics Statistics 12 Instructor: Nicolas Christou First: Population mean, µ: The central limit theorem The distribution of the sample mean Sample
More informationSection Introduction to Normal Distributions
Section 6.1-6.2 Introduction to Normal Distributions 2012 Pearson Education, Inc. All rights reserved. 1 of 105 Section 6.1-6.2 Objectives Interpret graphs of normal probability distributions Find areas
More informationChapter 8 Estimation
Chapter 8 Estimation There are two important forms of statistical inference: estimation (Confidence Intervals) Hypothesis Testing Statistical Inference drawing conclusions about populations based on samples
More informationAP Statistics Ch 8 The Binomial and Geometric Distributions
Ch 8.1 The Binomial Distributions The Binomial Setting A situation where these four conditions are satisfied is called a binomial setting. 1. Each observation falls into one of just two categories, which
More informationChapter 6. The Normal Probability Distributions
Chapter 6 The Normal Probability Distributions 1 Chapter 6 Overview Introduction 6-1 Normal Probability Distributions 6-2 The Standard Normal Distribution 6-3 Applications of the Normal Distribution 6-5
More informationBinomial Distributions
Binomial Distributions Binomial Experiment The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials There are only two possible outcomes of interest
More informationChapter 6 Confidence Intervals Section 6-1 Confidence Intervals for the Mean (Large Samples) Estimating Population Parameters
Chapter 6 Confidence Intervals Section 6-1 Confidence Intervals for the Mean (Large Samples) Estimating Population Parameters VOCABULARY: Point Estimate a value for a parameter. The most point estimate
More informationMidTerm 1) Find the following (round off to one decimal place):
MidTerm 1) 68 49 21 55 57 61 70 42 59 50 66 99 Find the following (round off to one decimal place): Mean = 58:083, round off to 58.1 Median = 58 Range = max min = 99 21 = 78 St. Deviation = s = 8:535,
More informationMath Week in Review #10. Experiments with two outcomes ( success and failure ) are called Bernoulli or binomial trials.
Math 141 Spring 2006 c Heather Ramsey Page 1 Section 8.4 - Binomial Distribution Math 141 - Week in Review #10 Experiments with two outcomes ( success and failure ) are called Bernoulli or binomial trials.
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability
More information. 13. The maximum error (margin of error) of the estimate for μ (based on known σ) is:
Statistics Sample Exam 3 Solution Chapters 6 & 7: Normal Probability Distributions & Estimates 1. What percent of normally distributed data value lie within 2 standard deviations to either side of the
More information8.1 Binomial Distributions
8.1 Binomial Distributions The Binomial Setting The 4 Conditions of a Binomial Setting: 1.Each observation falls into 1 of 2 categories ( success or fail ) 2 2.There is a fixed # n of observations. 3.All
More informationStudy Guide: Chapter 5, Sections 1 thru 3 (Probability Distributions)
Study Guide: Chapter 5, Sections 1 thru 3 (Probability Distributions) Name SHORT ANSWER. 1) Fill in the missing value so that the following table represents a probability distribution. x 1 2 3 4 P(x) 0.09
More informationSTA 6166 Fall 2007 Web-based Course. Notes 10: Probability Models
STA 6166 Fall 2007 Web-based Course 1 Notes 10: Probability Models We first saw the normal model as a useful model for the distribution of some quantitative variables. We ve also seen that if we make a
More informationMidterm Test 1 (Sample) Student Name (PRINT):... Student Signature:... Use pencil, so that you can erase and rewrite if necessary.
MA 180/418 Midterm Test 1 (Sample) Student Name (PRINT):............................................. Student Signature:................................................... Use pencil, so that you can erase
More informationLecture 23. STAT 225 Introduction to Probability Models April 4, Whitney Huang Purdue University. Normal approximation to Binomial
Lecture 23 STAT 225 Introduction to Probability Models April 4, 2014 approximation Whitney Huang Purdue University 23.1 Agenda 1 approximation 2 approximation 23.2 Characteristics of the random variable:
More informationChapter 5. Discrete Probability Distributions. McGraw-Hill, Bluman, 7 th ed, Chapter 5 1
Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7 th ed, Chapter 5 1 Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation
More informationThe Normal Approximation to the Binomial
Lecture 16 The Normal Approximation to the Binomial We can calculate l binomial i probabilities bbilii using The binomial formula The cumulative binomial tables When n is large, and p is not too close
More informationVersion A. Problem 1. Let X be the continuous random variable defined by the following pdf: 1 x/2 when 0 x 2, f(x) = 0 otherwise.
Math 224 Q Exam 3A Fall 217 Tues Dec 12 Version A Problem 1. Let X be the continuous random variable defined by the following pdf: { 1 x/2 when x 2, f(x) otherwise. (a) Compute the mean µ E[X]. E[X] x
More informationWhat is the probability of success? Failure? How could we do this simulation using a random number table?
Probability Ch.4, sections 4.2 & 4.3 Binomial and Geometric Distributions Name: Date: Pd: 4.2. What is a binomial distribution? How do we find the probability of success? Suppose you have three daughters.
More informationInstructor: A.E.Cary. Math 243 Exam 2
Name: Instructor: A.E.Cary Instructions: Show all your work in a manner consistent with that demonstrated in class. Round your answers where appropriate. Use 3 decimal places when rounding answers. In
More informationAnswer Key: Quiz2-Chapter5: Discrete Probability Distribution
Economics 70: Applied Business Statistics For Economics & Business (Summer 01) Answer Key: Quiz-Chapter5: Discrete Probability Distribution The number of electrical outages in a city varies from day to
More informationChapter 8. Binomial and Geometric Distributions
Chapter 8 Binomial and Geometric Distributions Lesson 8-1, Part 1 Binomial Distribution What is a Binomial Distribution? Specific type of discrete probability distribution The outcomes belong to two categories
More information4.1 Probability Distributions
Probability and Statistics Mrs. Leahy Chapter 4: Discrete Probability Distribution ALWAYS KEEP IN MIND: The Probability of an event is ALWAYS between: and!!!! 4.1 Probability Distributions Random Variables
More informationDiscrete Probability Distribution
1 Discrete Probability Distribution Key Definitions Discrete Random Variable: Has a countable number of values. This means that each data point is distinct and separate. Continuous Random Variable: Has
More information3/28/18. Estimation. Focus Points. Focus Points. Estimating p in the Binomial Distribution. Estimating p in the Binomial Distribution. Section 7.
Which side of a cheetah has the most spots? Estimation The outside. 7 Section 7.3 Estimating p in the Binomial Distribution Boy, I m tired. I ve been up since the quack of dawn. Focus Points Compute the
More informationSection 8.1 Estimating μ When σ is Known
Chapter 8 Estimation Name Section 8.1 Estimating μ When σ is Known Objective: In this lesson you learned to explain the meanings of confidence level, error of estimate, and critical value; to find the
More informationChapter 6 Confidence Intervals
Chapter 6 Confidence Intervals Section 6-1 Confidence Intervals for the Mean (Large Samples) VOCABULARY: Point Estimate A value for a parameter. The most point estimate of the population parameter is the
More information6.5: THE NORMAL APPROXIMATION TO THE BINOMIAL AND
CD6-12 6.5: THE NORMAL APPROIMATION TO THE BINOMIAL AND POISSON DISTRIBUTIONS In the earlier sections of this chapter the normal probability distribution was discussed. In this section another useful aspect
More informationProblem Set 07 Discrete Random Variables
Name Problem Set 07 Discrete Random Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the random variable. 1) The random
More informationData Analysis and Statistical Methods Statistics 651
Review of previous lecture: Why confidence intervals? Data Analysis and Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasini/teaching.html Suhasini Subba Rao Suppose you want to know the
More informationIf the distribution of a random variable x is approximately normal, then
Confidence Intervals for the Mean (σ unknown) In many real life situations, the standard deviation is unknown. In order to construct a confidence interval for a random variable that is normally distributed
More information1. [10 points] For a standard normal distribution. Find the indicated probability. For each case, draw a sketch. (a). (3 points) P( z < 152.
Spring 2007 Math 227 Test #3 Name: Show all necessary work NEATLY, UNDERSTANDABLY and SYSTEMATICALLY for full points. Any understatement and/or false statement may be penalized. This is a closed book,
More informationThe Central Limit Theorem
Section 6-5 The Central Limit Theorem I. Sampling Distribution of Sample Mean ( ) Eample 1: Population Distribution Table 2 4 6 8 P() 1/4 1/4 1/4 1/4 μ (a) Find the population mean and population standard
More informationChapter 6: Random Variables. Ch. 6-3: Binomial and Geometric Random Variables
Chapter : Random Variables Ch. -3: Binomial and Geometric Random Variables X 0 2 3 4 5 7 8 9 0 0 P(X) 3???????? 4 4 When the same chance process is repeated several times, we are often interested in whether
More informationChapter 5. Sampling Distributions
Lecture notes, Lang Wu, UBC 1 Chapter 5. Sampling Distributions 5.1. Introduction In statistical inference, we attempt to estimate an unknown population characteristic, such as the population mean, µ,
More informationMATH 104 CHAPTER 5 page 1 NORMAL DISTRIBUTION
MATH 104 CHAPTER 5 page 1 NORMAL DISTRIBUTION We have examined discrete random variables, those random variables for which we can list the possible values. We will now look at continuous random variables.
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 6 Normal Probability Distributions 6-1 Overview 6-2 The Standard Normal Distribution
More informationBinomial and Normal Distributions. Example: Determine whether the following experiments are binomial experiments. Explain.
Binomial and Normal Distributions Objective 1: Determining if an Experiment is a Binomial Experiment For an experiment to be considered a binomial experiment, four things must hold: 1. The experiment is
More informationStatistics Class 15 3/21/2012
Statistics Class 15 3/21/2012 Quiz 1. Cans of regular Pepsi are labeled to indicate that they contain 12 oz. Data Set 17 in Appendix B lists measured amounts for a sample of Pepsi cans. The same statistics
More informationAP Statistics Section 6.1 Day 1 Multiple Choice Practice. a) a random variable. b) a parameter. c) biased. d) a random sample. e) a statistic.
A Statistics Section 6.1 Day 1 ultiple Choice ractice Name: 1. A variable whose value is a numerical outcome of a random phenomenon is called a) a random variable. b) a parameter. c) biased. d) a random
More informationChapter 14 - Random Variables
Chapter 14 - Random Variables October 29, 2014 There are many scenarios where probabilities are used to determine risk factors. Examples include Insurance, Casino, Lottery, Business, Medical, and other
More informationDensity curves. (James Madison University) February 4, / 20
Density curves Figure 6.2 p 230. A density curve is always on or above the horizontal axis, and has area exactly 1 underneath it. A density curve describes the overall pattern of a distribution. Example
More informationThe Central Limit Theorem. Sec. 8.2: The Random Variable. it s Distribution. it s Distribution
The Central Limit Theorem Sec. 8.1: The Random Variable it s Distribution Sec. 8.2: The Random Variable it s Distribution X p and and How Should You Think of a Random Variable? Imagine a bag with numbers
More informationUnit2: Probabilityanddistributions. 3. Normal and binomial distributions
Announcements Unit2: Probabilityanddistributions 3. Normal and binomial distributions Sta 101 - Fall 2017 Duke University, Department of Statistical Science Formatting of problem set submissions: Bad:
More informationHomework Problems In each of the following situations, X is a count. Does X have a binomial distribution? Explain. 1. You observe the gender of the next 40 children born in a hospital. X is the number
More informationBinomial and Geometric Distributions
Binomial and Geometric Distributions Section 3.2 & 3.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Office hours: T Th 2:30 pm - 5:15 pm 620 PGH Department of Mathematics University of Houston February 11, 2016
More informationQM353: Business Statistics. Chapter 2
QM353: Business Statistics Chapter 2 1. The administrator at Saint Frances Hospital is concerned about the amount of overtime the nursing staff is incurring and wonders whether so much overtime is really
More informationBinomial Random Variables
Models for Counts Solutions COR1-GB.1305 Statistics and Data Analysis Binomial Random Variables 1. A certain coin has a 25% of landing heads, and a 75% chance of landing tails. (a) If you flip the coin
More informationMATH 264 Problem Homework I
MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that the
More information6.3: The Binomial Model
6.3: The Binomial Model The Normal distribution is a good model for many situations involving a continuous random variable. For experiments involving a discrete random variable, where the outcome of the
More information2) There is a fixed number of observations n. 3) The n observations are all independent
Chapter 8 Binomial and Geometric Distributions The binomial setting consists of the following 4 characteristics: 1) Each observation falls into one of two categories success or failure 2) There is a fixed
More informationStatistics for Business and Economics: Random Variables:Continuous
Statistics for Business and Economics: Random Variables:Continuous STT 315: Section 107 Acknowledgement: I d like to thank Dr. Ashoke Sinha for allowing me to use and edit the slides. Murray Bourne (interactive
More informationMath 230 Exam 2 Name April 8, 1999
Math 230 Exam 2 Name April 8, 1999 Instructions: Answer each question to the best of your ability. Most questions require that you give a concluding or summary statement. These statements should be complete
More informationHOMEWORK: Due Mon 11/8, Chapter 9: #15, 25, 37, 44
This week: Chapter 9 (will do 9.6 to 9.8 later, with Chap. 11) Understanding Sampling Distributions: Statistics as Random Variables ANNOUNCEMENTS: Shandong Min will give the lecture on Friday. See website
More informationProbability Distributions. Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution
Probability Distributions Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution Definitions Random Variable: a variable that has a single numerical value
More information1. The data in the following table represent the number of miles per gallon achieved on the highway for compact cars for the model year 2005.
Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Test 2 March 5, 2010, 10:00AM-10:50AM Please answer the following questions. Your answers will be evaluated
More informationChapter. Section 4.2. Chapter 4. Larson/Farber 5 th ed 1. Chapter Outline. Discrete Probability Distributions. Section 4.
Chapter Discrete Probability s Chapter Outline 1 Probability s 2 Binomial s 3 More Discrete Probability s Copyright 2015, 2012, and 2009 Pearson Education, Inc 1 Copyright 2015, 2012, and 2009 Pearson
More informationBinomal and Geometric Distributions
Binomal and Geometric Distributions Sections 3.2 & 3.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 7-2311 Cathy Poliak, Ph.D. cathy@math.uh.edu
More information7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4
7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. -
More informationMath 160 Professor Busken Chapter 5 Worksheets
Math 160 Professor Busken Chapter 5 Worksheets Name: 1. Find the expected value. Suppose you play a Pick 4 Lotto where you pay 50 to select a sequence of four digits, such as 2118. If you select the same
More informationUnit2: Probabilityanddistributions. 3. Normal and binomial distributions
Announcements Unit2: Probabilityanddistributions 3. Normal and binomial distributions Sta 101 - Summer 2017 Duke University, Department of Statistical Science PS: Explain your reasoning + show your work
More informationSection 7-2 Estimating a Population Proportion
Section 7- Estimating a Population Proportion 1 Key Concept In this section we present methods for using a sample proportion to estimate the value of a population proportion. The sample proportion is the
More informationWebAssign Math 3680 Homework 5 Devore Fall 2013 (Homework)
WebAssign Math 3680 Homework 5 Devore Fall 2013 (Homework) Current Score : 135.45 / 129 Due : Friday, October 11 2013 11:59 PM CDT Mirka Martinez Applied Statistics, Math 3680-Fall 2013, section 2, Fall
More informationNormal distribution. We say that a random variable X follows the normal distribution if the probability density function of X is given by
Normal distribution The normal distribution is the most important distribution. It describes well the distribution of random variables that arise in practice, such as the heights or weights of people,
More informationChapter 7. Sampling Distributions
Chapter 7 Sampling Distributions Section 7.1 Sampling Distributions and the Central Limit Theorem Sampling Distributions Sampling distribution The probability distribution of a sample statistic. Formed
More informationCHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS
CHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS A random variable is the description of the outcome of an experiment in words. The verbal description of a random variable tells you how to find or calculate
More informationApplications of the Central Limit Theorem
Applications of the Central Limit Theorem Application 1: Assume that the systolic blood pressure of 30-year-old males is normally distributed with mean μ = 122 mmhg and standard deviation σ = 10 mmhg.
More informationBusiness Statistics. Chapter 5 Discrete Probability Distributions QMIS 120. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should
More informationDO NOT POST THESE ANSWERS ONLINE BFW Publishers 2014
Section 6.3 Check our Understanding, page 389: 1. Check the BINS: Binary? Success = get an ace. Failure = don t get an ace. Independent? Because you are replacing the card in the deck and shuffling each
More informationchapter 13: Binomial Distribution Exercises (binomial)13.6, 13.12, 13.22, 13.43
chapter 13: Binomial Distribution ch13-links binom-tossing-4-coins binom-coin-example ch13 image Exercises (binomial)13.6, 13.12, 13.22, 13.43 CHAPTER 13: Binomial Distributions The Basic Practice of Statistics
More informationChapter 5 Normal Probability Distributions
Chapter 5 Normal Probability Distributions Section 5-1 Introduction to Normal Distributions and the Standard Normal Distribution A The normal distribution is the most important of the continuous probability
More informationPart 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?
1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard
More informationChapter 4 Probability Distributions
Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5
More informationChapter 5 Student Lecture Notes 5-1. Department of Quantitative Methods & Information Systems. Business Statistics
Chapter 5 Student Lecture Notes 5-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals
More informationUniversity of California, Los Angeles Department of Statistics. Normal distribution
University of California, Los Angeles Department of Statistics Statistics 110A Instructor: Nicolas Christou Normal distribution The normal distribution is the most important distribution. It describes
More informationChapter 4. Section 4.1 Objectives. Random Variables. Random Variables. Chapter 4: Probability Distributions
Chapter 4: Probability s 4. Probability s 4. Binomial s Section 4. Objectives Distinguish between discrete random variables and continuous random variables Construct a discrete probability distribution
More informationBinomial formulas: The binomial coefficient is the number of ways of arranging k successes among n observations.
Chapter 8 Notes Binomial and Geometric Distribution Often times we are interested in an event that has only two outcomes. For example, we may wish to know the outcome of a free throw shot (good or missed),
More informationChapter Six Probability Distributions
6.1 Probability Distributions Discrete Random Variable Chapter Six Probability Distributions x P(x) 2 0.08 4 0.13 6 0.25 8 0.31 10 0.16 12 0.01 Practice. Construct a probability distribution for the number
More informationSTA258H5. Al Nosedal and Alison Weir. Winter Al Nosedal and Alison Weir STA258H5 Winter / 41
STA258H5 Al Nosedal and Alison Weir Winter 2017 Al Nosedal and Alison Weir STA258H5 Winter 2017 1 / 41 NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION. Al Nosedal and Alison Weir STA258H5 Winter 2017
More informationUsing the Central Limit
Using the Central Limit Theorem By: OpenStaxCollege It is important for you to understand when to use the central limit theorem. If you are being asked to find the probability of the mean, use the clt
More informationChapter 8. Variables. Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc.
Chapter 8 Random Variables Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc. 8.1 What is a Random Variable? Random Variable: assigns a number to each outcome of a random circumstance, or,
More informationHonors Statistics. Aug 23-8:26 PM. 1. Collect folders and materials. 2. Continue Binomial Probability. 3. Review OTL C6#11 homework
Honors Statistics Aug 23-8:26 PM 1. Collect folders and materials 2. Continue Binomial Probability 3. Review OTL C6#11 homework 4. Binomial mean and standard deviation 5. Past Homework discussion 6. Return
More informationStats SB Notes 4.2 Completed.notebook February 22, Feb 21 11:39 AM. Chapter Outline
Stats SB Notes 42 Completednotebook February 22, 2017 Chapter 4 Discrete Probability Distributions Chapter Outline 41 Probability Distributions 42 Binomial Distributions 43 More Discrete Probability Distributions
More information1. Find the area under the standard normal distribution curve for each. (a) Between z = 0.19 and z = 1.23.
Statistics Test 3 Name: KEY 1 Find the area under the standard normal distribution curve for each a Between = 019 and = 123 normalcdf 019, 123 = 04660 b To the left of = 156 normalcdf 100, 156 = 00594
More informationStatistics 13 Elementary Statistics
Statistics 13 Elementary Statistics Summer Session I 2012 Lecture Notes 5: Estimation with Confidence intervals 1 Our goal is to estimate the value of an unknown population parameter, such as a population
More informationChapter 17 Probability Models
Chapter 17 Probability Models Overview Key Concepts Know how to tell if a situation involves Bernoulli trials. Be able to choose whether to use a Geometric or a Binomial model for a random variable involving
More informationMath 140 Introductory Statistics. Next midterm May 1
Math 140 Introductory Statistics Next midterm May 1 8.1 Confidence intervals 54% of Americans approve the job the president is doing with a margin error of 3% 55% of 18-29 year olds consider themselves
More information1. State Sales Tax. 2. Baggage Check
1. State Sales Tax A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6% with the additional revenue going to education. If 40% of all adults
More informationWeek 7. Texas A& M University. Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4
Week 7 Oğuz Gezmiş Texas A& M University Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4 Oğuz Gezmiş (TAMU) Topics in Contemporary Mathematics II Week7 1 / 19
More information