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. Question 1 The Lengths of pregnancies in a smalL rural village are normally distributed with a mean of 263.4 days and a standard deviation of 15.8 days. In what range would you expect to find the middle 68% of most pregnancies? Enter your answers as numbers. Your answers should be accurate to 1 decimal places. Check Answer . Question 2 In a large town, the size of the population is 600. 312 of the citizens own a car. [You may assume that all sampling is done WITH REPLACEMENT) 1. What is the proportion of the population that owns a car? [express the proportion as a decimal] :] 2. If one citizen is randomly selected from the population, what is the probability that the citizen owns a car? (express the probability as a decimal] :] 3. If one citizen is randomly selected from the population, what is the probability that the citizen does not own a car? (express the probability as a decimaL] :] 4. Ii 5 citizens are randomly selected from the population, what is the probability that all of them own a car? (you can round to 5 or more decimal places) :] 5. If 5 citizens are randomly selected from the population, what is the probability that exactly 3 own a car? (you can round to 5 or more decimal places] :] 6. If 5 citizens are randomly selected from the population, what is the probability that at least 3 own a car? (you can round to 5 or more decimal places) :] . Question 3 In Sick Town, 54% Of people have a cold, and 46% do not have a cold. It is a large population. We take a survey (sample) of 5 people from Sick Town, and we ask the question, "Do you have a cold?\" What is the probability that all say, "Yes"? :] What is the probability that not all say, "Yes"? :] What is the probability that all sayJ "No"? :] What is the probability that not all say, "No"? :] What is the probability that the sample responses contain a mixture of some "Yes" and some "No"? What is the probability that at least one person says, "Yes"? :] What is the probability that at least one person says, \"No"? :] Question 4 Test the claim that the mean GPA of night students is smaller than 3.2 at the 0.10 significance level. The null and alternative hypotheses would be: Ho:u = 3.2 Ho:p = 0.8 Ho:/ = 3.2 Ho:/ = 3.2 Ho:p = 0.8 Ho:p = 0.8 Hi:u > 3.2 Hi:p 0.8 O O The test is: left-tailed right-tailed two-tailed Based on a sample of 37 people, the sample mean GPA was 3.18 with a standard deviation of 0. 1 The p-value is: to 3 decimals) The significance level is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis. Question 5 Madison and Lauren are both trying to estimate the population mean u. Madison takes a sample of size n = 43 and uses or = 25.35. Madison's interval estimate: 7'1]