**QUESTION**

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Include work and box answers for full credit. Include a rough sketch of any graphs you use. Round your answers to the nearest third decimal place.

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Include work and box answers for full credit. Include a rough sketch of any graphs you use. Round your answers to the nearest third decimal place. 1. (15 points) Determine whether a linear model is appropriate for the given data set. Justify your answer. Include rough sketches of any graphs you reference. x 1.2 4.6 5.4 7.3 14.2 16 15.5 13.1 21.3 19.8 10.1 16.8 20 y 6 15 9 12 10 20 22 18 13 26 16 12 18

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1. (15 points) Determine whether a linear model is appropriate for the given data set. Justify your answer. Include rough sketches of any graphs you reference. x 1.2 4.6 5.4 7.3 14.2 16 15.5 13.1 21.3 19.8 10.1 16.8 20 y 6 15 9 12 10 20 22 18 13 26 16 12 18

2. (20 points) Suppose the following data lists the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket. Assume that a linear model is appropriate for the data. a. Find an equation for the least squares regression line treating temperature as the explanatory variable and chirps per second as the response. b. Interpret the slope. If it is not appropriate to interpret the slope, explain why. c. Interpret the y-intercept. If it is not appropriate to interpret the y intercept, explain why. d. Find and interpret the correlation coefficient and coefficient of determination. e. Predict the chirps per second if the temperature is 72.3 °F. f. For what range of temperatures is it appropriate to use the linear model to predict the number of chirps per second? Justify your answer.

3. (15 points) Suppose that a local second hand store is selling grab bags for $20 each in order to get rid of excess stock. They have created a total of 300 grab bags, most of which contain various items worth $15 in total. However, there are 40 grab bags which contain items worth $40 in total, 20 grab bags worth $60 in total, and a single grab bath worth $120 in total. Suppose you purchase one grab bag. Let X be the monetary value of a grab bag. a. Create a discrete probability distribution for X. b. Find and interpret the mean for X. c. Find the standard deviation for X. d. Is it worthwhile to purchase a grab bag? Justify your answer.

4. (15 points) Suppose that a certain food company holds a promotion with their popsicles, in which 30% of all of their popsicle sticks have “Winner” printed on them. The popsicles can be turned in for various prizes. Suppose a certain group of friends pools their resources to buy 70 popsicles over the course of the promotion. a. Explain why a binomial distribution is appropriate to describe the number of Winner sticks the friends could obtain. b. Find and interpret the mean of the number of Winner sticks obtained. c. Find the standard deviation of the number of Winner sticks obtained. d. Find and interpret the probability of the friends obtaining 25 Winner sticks. e. Suppose that the friends want at least 30 Winner sticks to redeem one of the prizes. Would it be considered unusual for them to be able to redeem the prize? Justify your answer.

5. (20 points) In a survey of 56,629 American adults, a relative frequency distribution for the religious preferences of four age groups are shown in the following table. Use this information to answer the following questions. 19-30 (Years Old) 31-40 (Years Old) 41-55 (Years Old) 56-89 (Years Old) Total Protestant .117 .114 .153 .197 .581 Catholic .066 .057 .065 .069 .257 Other .014 .015 .016 .012 .057 None .039 .026 .023 .017 .105 Total .236 .212 .257 .295 1

a. Does there appear to be an association between age and religious preferences? Justify your answer. b. Find the probability that a randomly selected Catholic is aged 56-89. c. Find the probability that a randomly selected individual is aged 19-30 or has no religious preference. d. Is having a religious preference of Catholic independent from being aged 31-40? Are these events mutually exclusive? Justify your answers.

6. (15 points) Harold has a collection of 20 movies that he wants to organize. a. There is a set of small shelves that can store media at the foot of Harold’s bed. If each shelf can store up to 5 movies, how many different ways could movies be lined up on a shelf (if the shelf is going to be full)? b. A friend of Harold’s asked to borrow some movies. How many different ways can Harold lend his friend 3 movies? c. Unknown to Harold, his friend does not own a Blu-ray player. If 6 of Harold’s movies are stored on Blu-ray, what is the probability that at least one of the 3 movies Harold lends to his friend is on Blu-ray?

**ANSWER**