Question

Average height of men is normally distributed with mean height of 160 cm and standard deviation of 5 cm. If a sample of 9 men are randomly selected from this population, find the probability that the mean is between 155 cm and 160 cm. Question 20 options: 0.3412 0.50 0.0013 0.4987 0.5821

Answer 1

Given,

= 160 , = 5

using central limit theorem,

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

So,

P(155 < < 160) = P( < 160) - P( < 155)

= P(Z < 160 - 160 / (5 / sqrt(9) ) ) - P( Z < 155 - 160 / (5 / sqrt(9) ) )

= P(Z < 0) - P(Z < -3)

= 0.5 - 0.0013

= 0.4987