Question

The heights of South African men are Normally distributed with a mean of 69 inches and a standard deviation of 4 inches. Reference: Ref 6-1 If a random sample of three South African men were selected at random, what is the probability that the sample mean height is greater than 72 inches?

A.0.2266 B.0.0122

C. 0.0968 D.0.9032

Answer 1

Solution :

Given that ,

mean = = 69

standard deviation = = 4

n = 3

= = 69 and

= / n = 4 / 3 = 2.3094

P( > 72) = 1 - P( < 72)

= 1 - P(( - ) / < (72 - 69) / 2.3094)

= 1 - P(z < 1.30)

= 1 - 0.9032 Using standard normal table.

= 0.0968

Probability = 0.0968

Option C is correct.