Question

Heights of a basketball team are known to not be normally distributed. The team heights have a mean of 7.1ft and the standard deviation 1.5 ft. a) Find the probability that 36 players have a mean height between 6.2 ft and 7.5 ft. b) Explain why, for part a, you were able to use the Central Limit Theorem to solve the problem.

Answer 1

We have X : height of basketball team has mean = 7.1 ft and standard deviation = 1.5 ft

a) if n = 36 we asked P( 6.2 < xbar < 7.5)

P(6.2 < xbar < 7.5) =P[( 6.2-/√n) < (xbar -/√n) < ( 7.5 - /√n)]

P(6.2 < xbar < 7.5) = P( -3.60 < Z < 1.60)

= P( Z < 1.60) - P( Z < -3.60)

P( 6.2 < xbar < 7.5) = 0.9452 - 0.0002

P( 6.2 < xbar < 7.5) = 0.9450

b)

In part a) we used the central limit theorem because the sample size n > 30