Question

Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches. Write your answer as a decimal rounded to 4 places.

Answer 1

Solution :

Given that ,

mean = = 63.6

standard deviation = = 2.5

P(62.9 < x < 64) = P((62.9 - 63.6)/ 2.5) < (x - ) /  < (64 - 63.6) / 2.5) )

= P(-0.28 < z < 0.16)

= P(z < 0.16) - P(z < -0.28)

= 0.5636 - 0.3897

= 0.1739

Probability = 0.1739