Bobs height is 74 in In his sport team the mean height is 71

Bob’s height is 74 in.
In his sport team, the mean height is 71 in, and the standard deviation is 3 in.
Jeff’s height is 76 in.
In his sport team, the mean height is 73 in, and the standard deviation is 2.8 in.
Chris’ height is 75 in.
In his sport team, the mean height is 69 in, and the standard deviation is 2.6 in.

Is any of them unusually tall in his sport team? Justify your answer.

Solution

consider the height to follow a normal distribution.

For Bob.

Percentage of men below his height = P(X<74) = P(Z<(74-71)/3) = P(Z<1)= 84.13%

For Jeff

Percentage of men below his height = P(X<76 ) = P(Z< (76-73)/2.8) = P(Z<1.07 ) = 85.77%.

For Chris

Percentage of men below his height = P(X<75) = P(Z<(75-69)/2.6) = P(Z<2.31) = 98.96%.

From above we can see that Chris is unsusually tall in his sports team.