Suppose that a resistance of a certain 100-ohm resistor is normally distributed with mean 100 ohms and standard deviation 8.7 ohms. Assume that each resistor's resistance is independent of each other. Part I. Suppose that a quality control engineer randomly selects 10 of these resistors and measures their resistance individually. (a) Define Y, = resistance measurement of the i-th resistor where i = 1, 2, ..., 10. Then 7 = By is the sample mean resistance of these 10 resistors. What are the mean, variance, and standard deviation of 77 If necessary, round your answer to three decimal places. E(Y)= V(Y)= (b) Select the statement that correctly describes the sampling distribution of y. Think carefully before submitting your answer, you only have two tries for this part. y always follows a normal distribution. Since the sample size is large enough, y approximately follows a normal distribution by Central Limit Theorem. The sample size is not large enough for us to use the Central Limit Theorem; the distribution of y is unknown. Since each resistance measurement is a normal random variable, y follows a normal distribution. Since the sample size is large enough, 7 follows a normal distribution by Central Limit Theorem. (c) What is the probability that the mean resistance of those 10 resistors is within 96.5 ohms and 98.9 ohms. Enter "NA" if the probability cannot be obtained. (d) What is the probability that the mean resistance of those 10 resistors is greater than 103.3 ohms. Enter "NA" if the probability cannot be obtained. Part II. Now suppose that a quality control engineer randomly selects 40 of these resistors and measures their resistance individually. istor where i = 1, 2, ...40. Then 8 = (a) Define X, = resistance measurement of the i-th resistor where i = 1, 2, ..., 40. Then X = 3 x is the sample mean resistance of x is the sample mean resistance of these 40 resistors. What are the mean, variance, and standard deviation of X? If necessary, round your answer to five decimal places. E(X)= V(x)= 07= (b) Select the statement that correctly describes the sampling distribution of X. Think carefully before submitting your answer, you only have two tries for this part. Since the sample size is large enough, follows a normal distribution by Central Limit Theorem. Since the sample size is large enough, approximately follows a normal distribution by Central Limit Theorem. Since each resistance measurement is a normal random variable, follows a normal distribution. X always follows a normal distribution. The sample size is not large enough for us to use the Central Limit Theorem; the distribution of is unknown. (c) What is the probability that the mean resistance of those 40 resistors is within 96.5 ohms and 98.9 ohms. Enter "NA" if the probability cannot be obtained. (d) What is the probability that the mean resistance of those 40 resistors is greater than 103.3 ohms. Enter "NA" if the probability cannot be obtained. You may need to use the appropriate table in the Appendix of Tables to answer this question.