Question

A simple random sample of size n = 81 is obtained from a population with u = 70 and o = 27. (a) Describe the sampling distribution of x. (b) What is P (X>73)? (c) What is P (7562.5) ? (d) What is P (67.9<x< 75.25)?

Answer 1

Given that, mean (μ) = 70 and standard deviation $(\sigma)$ = 27

sample size (n) = 81

a) Since, the sample size is large, the sampling distribution of the sample mean is approximately normal.

(1)

The mean and standard deviation of the sampling distribution of the sample means are,

(1)

Hi = p = 70

27 01 3 이트 12 V81

b) We want to find,

PT> 73

PT > 73) 73 – 70 = PC > 0 3 = P(Z > 1) = 1 - P(Z < 1) = 1-0.8413 = 0.1587

=> PT > 73) = 0.1587

c) We want to find,

PT < 62.5)

PT < 62.5) = PC 62.5 – 70 - 0 3 = P(Z < -2.5) =1 - P(Z < 2.5) = 1-0.9938 = 0.0062

=> PT < 62.5) = 0.0062

d) We want to find,

P(67.9<< 75.25)

=> P(67.9 <> 75.25) = 0.7179