Question

Assume the heights of men are normally distributed, with mean 73 inches and standard deviation 4 inches. If a random sample of nine men is selected, what is the probability that the mean height is between 72 and 74 inches? (Use 3 decimal places.)

Answer 1

Given,

= 73, = 4

Using central limit theorem,

P( < x) = P(Z < ( x - ) / ( / sqrt(n) ) )

So,

P(72 < < 74) = P( < 4) - P( < 72)

= P(Z < (74 - 73) / (4 / sqrt(9) ) ) - P(Z < (72 - 73) / (4 / sqrt(9) ) )

= P(Z < 0.75) - P(Z < -0.75)

= 0.7734 - 0.2266 (From Z table)

= 0.547