1. The length of human pregnancies is approximately normally distributed with mean u = 266 days and standard deviation 0 = 16 days. a. What is the probability a randomly selected pregnancy lasts less than 260 days? Provide a sketch. b. Find the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less. c. Find the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or more. 2. CIarinexD is a medication whose purpose is to reduce symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. a. If 240 users of Clarinex-D are randomly selected, how many would we expect to experience insomnia as a side effect? HINT: Recall binomial RVs. b. Is up > 5? Is n(1 p) > 5? What tool do these criteria allow us do utilize? c. Use a normal approximation to calculate the probability of observing 20 or more patients experiencing insomnia as a side effect in 240 trials. Would this be considered unusual? Why? 3. A researcher at an agricultural experiment station would like to measure the butterfat production for certain dairy cattle when inorganic nitrate is added to their diet. She would like to estimate the mean butterfat production for this treatment group. A 95% confidence interval for the mean butterfat production, based on a random sample of 40 dairy cattle, was calculated to be (433.64 , 496.36). a. Does the population mean lie in the interval (433.64 , 496.36)? b. Does the sample mean lie in the interval (433.64 , 496.36)? c. What is the value of the sample mean? d. If she uses a 99% level of confidence, will the confidence interval from the same data produce an interval narrower than {433.64 , 496.36)? Why or why not? 4. Use the t-table to find the following t-values: a. t5'0_05 e. Ifcr = 0.01 and n = 11, find: '3 1725,0115 trifJ-'r and tde 9- t5,o.025 d t46,0.025 5. A new diet program claims that participants will lose, on average, at least 8 pounds by the end of the first week of the program. A random sample of 40 people participating in the program showed a sample mean weight loss of 7 pounds at the end of the first week. The sample standard deviation was 3.2 pounds. a. Calculate a 95% confidence interval for the true mean weight loss. b. What is your conclusion about the claim made by the diet program? Does their claim seem valid? 6. To check on a weight requirement for a shipment of apples, 30 apples were selected at random from the shipment and their weights in ounces were measured. The sample mean and standard deviation are 5.9 and 1.75, respectively. a. Find the 99% confidence interval for the population mean weight, 11. b. Without doing any calculations, what affect would increasing the sample size have on the 99% confidence interval from part A {all other things being equal}? 7. In a survey, 1100 adults in San Luis Obispo were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was: {41.6, 44.3) hours. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. a. 95% of adults in San Luis Obispo worked between 41.6 hours and 44.3 hours last week. b. We are 95% confident that the mean number of hours worked by adults in California in the previous week was between 41.5 hours and 44.3 hours. c. We are 95% confident that the mean number of hours worked by adults in San Luis Obispo in the previous week was between 41.5 hours and 44.3 hours. 8. In a survey of 3611 adult Americans 18 years and older conducted in July 2010 by Smart Revenue, it was found that 1542 have used their smartphone to make a purchase. a. Calculate the point estimate for the population proportion of adult Americans 18 years and older who have used their smartphone to make a purchase. b. Construct a 90% confidence interval for the population proportion of adult Americans who have used their smartphone to make a purchase. c. Interpret the interval. HINT: Consider #7. 9. Wendy, a candidate in a two-person election commissions a poll to determine who is ahead. The pollster randomly chooses 500 registered voters and determines that 260 out of the 500 favor Wendy. a. Obtain a point estimate for the population proportion of registered voters who prefer Wendy. b. Construct a 95% confidence interval for the population proportion of registered voters who prefer Wendy. c. Based on the Cl above, is there evidence that a majority of voters favor Wendy? 10. How do you know when to use of the t-table? When do we use of the Standard Normal z-table