Question

Assume that the heights of men are normally distributed with a mean of 69.3 inches and a standard deviation of 3.5 inches. If 100 men are randomly selected, find the probability that they have a mean height greater than 70.3 inches.

Answer 1

Solution :

Given that ,

mean = = 69.3

standard deviation = = 3.5

= / n = 3.5 / 100 = 0.35

P( > 70.3) = 1 - P( < 70.3)

= 1 - P[( - ) / < (70.3-69.3) /0.35 ]

= 1 - P(z < 2.86)

= 1 - 0.9979 = 0.0021,Probability = 0.0021