Question

Assume that the heights of men are normally distributed with a mean of 68.1 inches and a standard deviation of 2.8 inches. If 64 men are randomly​ selected, find the probability that they have a mean height greater than 69.1 inches.

​(Round your answer to three decimal places​.)

Answer 1

Solution :

Given that,

mean = = 68.1

standard deviation = = 2.8

n=64

= =68.1

= / n = 2.8 / 64 = 0.35

P( >69.1 ) = 1 - P( < 69.1)

= 1 - P[( - ) / < (69.1-68.1) / 0.35]

= 1 - P(z <2.86 )

Using z table

= 1 - 0.9979

probability= 0.0021