Question

A large amateur basketball league has an average height of 76 inches with a standard deviation of 1.8 inches

a. if one player is randomly selected, find prob that his height is over 78 inches

b. if 36 players are randomly selected, find prob that the mean height for the sample is over 78 inches

Answer 1

Here given that, a amateur basketball league has an average height of 76 inches with a standard deviation of 1.8 inches.

Let, X be the height of basketball league in inches. It follows normal distribution with mean 76 inches and S.D. 1.8 inches.

So pdf of X is as

here, we know the value of mean and s.d so pdf is as

a) P(player height is over 78 inches) = P(x>78) = 1 - P(X<= 78)

= 1 - 0.8665 = 0.1335

we take value of phi from following table

i.e. if one player is randomly selected, the prob that his height is over 78 inches is 0.1335

b) Here given that, n=36 and sample mean is 78. so here follows normal distribution with parameters (76, 1.8/6)

So, P(player mean for the sample height is over 78 inches) =

= 1 - 0.9999 = 0.0001

i.e. if 36 players are randomly selected, the prob that the height for the sample is over 78 inches is 0.0001