Question

The average height of professional basketball players is around 6 feet 7 inches, and the standard deviation is 3.89 inches. Assuming Normal distribution of heights within this group

(a) What percent of professional basketball players are taller than 7 feet?

(b) If your favorite player is within the tallest 20% of all players, what can his height be?

Answer 1

Solution :

Given that ,

mean = = 6 feet 7 in. = 79 in.

standard deviation = = 3.89 in.

a) P(x > 84) = 1 - p( x< 84)

=1- p P[(x - ) / < (84 - 79) / 3.89]

=1- P(z < 1.29)

Using z table,

= 1 - 0.9015

= 0.0985

The percentage is = 9.85%

b) Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20  

= P(Z < z ) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < 0.84) = 0.80  

z = 0.84

Using z-score formula  

= z * +

= 0.84 * 3.89 + 79

= 82.27 in.