1. State whether the following groups are populations or samples. You are encouraged to justify your answers.

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1 MATH 2210 Exam 1 Review Solution Note: This review is NOT comprehensive, so do not limit your study to it. 1. State whether the following groups are populations or samples. You are encouraged to justify your answers. Many of these could be considered either a population or a sample. You just have to justify it. a. All the counties in the state of Georgia This is a population since it includes all of the counties in Georgia, but it could also be a sample of counties in the US. b. Three scoops from a tub of ice cream This is a sample since it is just a portion of the ice cream from the tub. c. The 8 planets in our solar system This is the population since it includes all of the planets in our solar system, but it could also be considered a sample of the planets in the galaxy or universe (a convenience sample). d. AU students who are mathematics majors This is a population if it includes all math majors at AU, but it could also be considered a sample of all AU students or of math majors in Georgia or the US. e. 50 sea turtles tagged by a marine biologist This is a sample because it is a group of sea turtles that will be studied and it does not include all sea turtles. 2. State whether the following numbers are parameters or statistics. You are encouraged to justify your answers. a. the average salary of an NFL football player This could be either a parameter or a statistic. Since sampling isn t specifically mentioned, I would go with it as a parameter since it is certainly a number that describes the population of all NFL players. b. the average volume of the eggs in a dozen bought at Publix I would view this as a statistic since the dozen eggs is a sample, and the average volume would be calculated from data gathered from this sample. c. the approval rating of the president as reported in the media An approval rating reported in the media is generated from polling, so it is calculated from a sample and is therefore a statistic. d. the population of the United States This is a parameter since it describes a population.

2 Use the following data set for review problems 3 7 Females pulse rates Make a stemplot of the data. Thoroughly describe the distribution of the data The center of the distribution is in the high 70 s. The pulse rates range from a low of 56 to a high of 104. The distribution is roughly bell shaped. There are no outliers. 4. Make a frequency table of the data. Range Frequency Relative Frequency % % % % % % 5. Make a histogram of the data. This is straightforward with the frequency table. 6. Calculate the following statistics from the data a. median 77 b. 5 number summary 56, 72, 77, 82, 104 c. IQR IQR = 10 d. 65 th percentile 78 e. mean 77.5 f. standard deviation g. variance Draw a boxplot of the distribution. Use the 5 number summary.

3 8. Consider the following random process: You have an opaque fabric bag that contains 3 balls, one that is red, one yellow and one blue. The balls are identical except for their color. You reach into the bag without looking, draw out a ball and check its color. a. What is the sample space for this random process? {red, yellow, blue} b. What is the probability of the event draw the yellow ball? P(yellow) = 1/3 9. The following data is from a study comparing an aggressive approach to selling used cars with a passive approach. There were a total of 1160 sales attempts Sale No Sale Row Total Aggressive Passive Column Total a. Calculate P(Aggressive and Sale) b. Calculate P(Sale) c. Calculate P(Passive or No Sale) d. Calculate P(Sale Passive) Suppose the AU women s basketball team has a 0.4 chance to win, and the men s basketball team has a 0.85 chance to win. They are not playing each other. a. Do you think the events the women s team wins and the men s team wins are independent? Justify your answer. I would say they are independent, since one team winning is unlikely to affect the probability that the other team wins. b. Assuming these events are independent, what is the probability both teams win?

4 11a. Fred has a 90% chance to get an A in ENGL 1101 this semester, and he has an 8% chance to get a B. What is the probability that Fred will either get an A or a B in ENGL 1101 this semester? These events are mutually exclusive, so 90% + 8% = 98%. b. What is the probability that Fred will not get an A or a B in ENGL 1101 this semester? This is the complement of the event in part a, so the probability is 2%. c. Fred has a 90% chance to get an A in ENGL 1101, a 95% chance to get an A in COMS 1100, and an 87% chance to get an A in both courses. What is the probability that Fred gets an A in either ENGL 1101 or COMS 1100? 90% + 95% 87% = 98% 12. An unfair 6 sided die has the following probability distribution. Number Prob a. Find the value of the missing probability (makes the sum of all the probabilities 1). b. Find P(an odd number is rolled) = 0.4 c. Calculate the mean and standard deviation of the die s probability distribution d. Why did I describe this die as unfair? The outcomes are not all equally likely.

5 13. A survey found that 80% of consumers would prefer organically grown produce over those treated with fertilizers and pesticides. Suppose you ask a random sample of 15 people if they prefer organic produce, and let X = # who say they prefer organic produce. The distribution of X is 15, 0.8. a. Calculate P(X = 10) b. Calculate P(X 12) c. Calculate P(X 13) d. Calculate the mean µ and the standard deviation for the random variable X e. Suppose you did the sampling process described in this problem, and 3 people responded that they prefer organic produce. Is this result unusual or not? Justify your answer. Unusual. The probability that 3 or fewer people respond this way is Also, a response like this has a z score of 5.8.

Math 2311 Bekki George Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment

Math 2311 Bekki George Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Math 2311 Bekki George bekki@math.uh.edu Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Class webpage: http://www.math.uh.edu/~bekki/math2311.html Math 2311 Class