Question

6. Basic Computation: Central Limit Theorem Suppose x has a distribution with a mean of 20 and a standard deviation of 3. Random samples of size n 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 19. (c) Find P(x < 19). (d) Interpretation Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 19? Explain.

Answer 1

M = 20 8-3 n = 36 a) The sample size n=36 is greater than 30, so by using central limit theoerm 8 follows approximately Normal distribution, Mi = ll = 20 3 O.S b) Ž=19 Z- X-MX 19-20 64 z = -2 c ) P ( X <19) P(X-M7 19-20 2. O.S PL 2«. <-2.00) -2 P ( Y <19) 0.0228 from Normal distribution table is d) Yes it unusual for random sample of size 30 from a distribution to have sample mean less than Ig, because this probability is less than oos.