Study Guide: Chapter 5, Sections 1 thru 3 (Probability Distributions)

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1 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 P(x) ? ) Which of the following variables are discrete? i. the depth of a submarine ii. the number of torpedoes on a submarine iii. the speed of the submarine 3) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find P(1 or more). x P(x) ) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find the probability that a family took at least 3 vacations last year. x P(x)

2 5) The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for this data. Number of calls X Probability P(X) ) Find the mean of the distribution shown below. X P(X) ) Find the mean of the distribution shown below. X P(X) ) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean!. x P(x)

3 9) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the standard deviation σ. x P(x) ) Compute the mean of the random variable with the given discrete probability distribution. x P(x) ) Compute the standard deviation of the random variable with the given discrete probability distribution. x P(x) ) An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.1 of a $15,000 loss, probability 0.05 of a $20,000 loss, probability 0.4 of a $30,000 profit, and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit? 3

4 13) Compute the probability of X successes. n = 7, X = 6, p = ) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 12, p = 0.7, P(3) 15) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 11, p = 0.5, P(Fewer than 4) 16) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 15, p = 0.8, P(13 or more) 17) A student takes a true-false test that has 15 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(13 or more) 4

5 18) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 25% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 19 adult dogs is studied. What is the probability that no more than 3 of them weigh 65 lb or more? 19) It is estimated that 45% of households own a riding lawn mower. A sample of 10 households is studied. What is the probability that more than 7 of these own a riding lawn mower? 20) It is estimated that 45% of households own a riding lawn mower. A sample of 16 households is studied. What is the mean number of households who own a riding mower? 21) It is estimated that 35% of households own a riding lawn mower. A sample of 14 households is studied. What is the standard deviation of the number of households who own a riding lawn mower? 22) A student takes a 14-question, multiple-choice exam with four choices for each question and guesses on each question. Find the probability of guessing exactly 7 out of 14 correctly. 5

6 23) Find the mean for the values of n and p when the conditions for the binomial distribution are met. n = 200, p = ) Find the variance for the values of n and p when the conditions for the binomial distribution are met. n = 100, p = ) Find the standard deviation for the values of n and p when the conditions for the binomial distribution are met. n = 900, p = ) In a survey, 65% of the voters support a particular referendum. If 40 voters are chosen at random, find the standard deviation of the number of voters who support the referendum. 27) A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week? 6

7 28) A university has 10,000 students of which 45% are male and 55% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students. 29) A school is sending 13 children to a camp. If 10% of the children in the school are first graders, and the 13 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen? 30) 56% of men do not look forward to going clothes shopping for themselves. You randomly select eight men. (a) Find the probability that exactly five men do not look forward to going clothes shopping for themselves. (b) Find the probability that more than five men do not look forward to going clothes shopping for themselves. (c) Find the probability that at most five men do not look forward to going clothes shopping for themselves. 7

8 Answer Key Testname: STUDY GUIDE CH 5 SEC 1 TO 3 1) ) ii 3) ) ) 6) ) ) ) ) ) ) $ ) ) ) ) ) ) ) ) ) ) ) ) ) ) The standard deviation is ) ) Mean = 13.5, Variance = ) The mean is 1.3, and the variance is ) 0.263, 0.238,

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

First Name: Last Name: SID: Class Time: M Tu W Th math10 - HW3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Continuous random variables are