. Question 1 v A population of values has an unknown distribution with ,u. = 51.9 and a = 29.8. You intend to draw a random sample of size n = 245. What is the mean of the distribution of sample means? #5 = C] (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? or; = C] (Please report your answer accurate to 2 decimal places.) lQuestionz v Carolyn wants to find out: if the standard deviation of the mean for the sampling distribution of random samples of size 121 from a large or infinite population is 6, how large must the sample size become if the standard deviation is to be reduced to 1.4 (or even smaller)? C Question 3 v A leading magazine [like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 4 weeks. Suppose you would like to select a random sample of 36 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. Note: When writing the distributions, they should be of the form (mean, variance}. a. What is the distribution of X? b. What is the distribution of 5:? c. What is the probability that one randomly selected individual found a job more than 24 weeks? d. For 36 unemployed individuals, find the probability that the average time that they found the next job is more than 24 weeks. :] e. For part d], is the assumption of normal necessary? 0 N00 Yes . Question 4 v A company produces steel rods. The lengths of the steel rods are distributed with a mean of 201 -cm and a standard deviation of 1.2-cm. For shipment, 14 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X N I: 1 , b. What is the distribution of 5:? 119le .~ } c. For a single randomly selected steel rod, find the probability that the length is between 200.6-cm d. For a bundled of 14 rods, find the probability that the average length is between 200.6-cm and e. For part d), is the assumption of normal necessary? 0 N00 Yes