Question

Average height of men is normally distributed with mean height of 160 cm and standard deviation...

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

Homework Answers

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

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