ANSWER SHOULD INCLUDE STEPS AND EXCEL OUTPUT IF ANY Using central limit theorem. 1. Problem 5.18 Question a and b only Finding probabilities of sample mean(x)1.Problem 5.19 and 5.21
d. n - 50 proximately normal. C. N = 500 f. N = 1.000 e. Explain how the results of parts bed illustrate the Central Limit Theorem. 5.18 A random sample of a - 64 observations is drawn from ww a population with a mean equal to 20 and a standard deviation equal to 16. Applet Exercise 5.2 a. Give the mean and standard deviation of the (repeated) Open the applet Sampling Distributions. On the pull-down menu sampling distribution of 5. to the right of the top graph, select Uniform. The box to the left b. Describe the shape of the sampling distribution of J. of the top graph displays the population mean, median, and stan- Does your answer depend on the sample size? dard deviation of the original distribution. c. Calculate the standard normal z-score corresponding to a. Run the applet for the sample size n - 30 and the a value of * - 15.5. number of samples / - 1,000. Observe the shape of d. Calculate the standard normal c-score corresponding to the graph of the sample means and record the mean, J - 23. median, and standard deviation of the sample means 5.19 Refer to Exercise 5.18. Find the probability that b. How does the mean of the sample means compare with NW a. V is less than 16. the mean of the original distribution? b. $ is greater than 23. c. Divide the standard deviation of the original distribution a $ is greater than 25. by V30, the square root of the sample size used in the d. F falls between 16 and 22. sampling distribution. How does this result compare with e. F is less than 14. the standard deviation of the sample proportions? 5.20 A random sample of n = 900 observations is selected d. Explain how the graph of the distribution of sample from a population with a = 100 and or = 10. means suggests that the distribution may be approxi- a. What are the largest and smallest values of * that you mately normal. would expect to see? c. Explain how the results of parts bed illustrate the b. How far, at the most, would you expect x to deviate Central Limit Theorem. from /t.? c. Did you have to know a to answer part b? Explain. Applying the Concepts-Basic 5.21 A random sample of a = 100 observations is selected 5.23 Voltage sags and swells. Refer to the Electrical Engineering from a population with a - 30 and o = 16. Approximate (Vol. 95, 2013) study of the power quality (sags and swells) the following probabilities: of a transformer, Exercise 2.76 (p. 110). For transformers a. P(F 2 24) built for heavy industry. the distribution of the number of b. P(22.1 = 1 = 268) sags per week has a mean of 353 with a standard deviation C. P(X = 28.2) of 30. Of interest is J. the sample mean number of sags per d. P(X = 27.0) wock for a random sample of 45 transformers. 5.21 Consider a population that contains values of a equal to 0, a. Find E(x) and interpret its value. h. Find Vanlil ENG
