Suppose x has a distribution with a mean of 80 and a standard deviation of 51. Random samples of size n - 36 are drawn. I USE SALT (a) Describe the x distribution and compute the mean and standard deviation of the distribution. has an approximately normal * distribution with mean - BO (b) Find the z value corresponding to x-88.5. and standard deviation - 51 (c) Find P(x < 88.5). (Round your answer to four decimal places.) P(x < 88.5) - (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 88.5? Explain. O Yes, it would be unusual because less than 5% of all such samples have means less than 88.5. O No, it would not be unusual because less than 5% of all such samples have means less than 88.5. O Yes, it would be unusual because more than 5% of all such samples have means less than 88.5. No, it would not be unusual because more than 5% of all such samples have means less than 88.5. Suppose x has a distribution with - 14 anda - 9. USE SALT (a) If a random sample of size n - 42 is drawn, find and P(14 x 16). (Round to two decimal places and the probability to four decimal places.) 1- R14 sxs 16) - (b) If a random sample of size n = 65 is drawn, find and P(14 sxs 16). (Round to two decimal places and the probability to four decimal places.) 1- R(145 x 516) - (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is -Select- part (a) because of the Select sample size. Therefore, the distribution about is-Select---