Question

The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e). 48 60 44 40 64 (a) Compute the population mean, H. u= 51.2 (b) Compute the mean for all C2 = 10 samples with size n=2. Sample Sample Mean 40.64 52 Sample Sample Mean 48,40 44 48,60 54 48,64 56 40.44 42 46 48,44 40.60 60,64 60,44 64,44 62 52 54 50 (c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities. Give all the unique sample means in ascending order. (Type N if there is no solution.) Probability Sample Mean 54 1 6 Probability 2 .1 .1 2 7 Sample Mean 42 44 46 50 52 56 1 .1 8 4 .1 9 n n 5 2 10 n n (d) Compute the mean of the sampling distribution. The mean of the sampling distribution is 51.2 years. (e) Compute the probability that the sample mean is within 2 years of the population mean age. The probability is

Answer 1

sal: (C) From the given data 7 X- 51.9 E 5 S = 10.3537 lo < Z < P(-2 10.3537/55 =P (-0.43 10.3537/15 0.43 < Z < 0.43) = P(Z <0.43) - P(Z <-0-43.) =P (Z<0.43) - 1 + P(Z <0.43) = g P(Z < 0.43) -1 = & *0.6664 -1 a 1.3398 -1 0.3328