The average height of professional basketball players is aro

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. What percent of professional basketball players are taller than 7 feet? If your favorite player is among the tallest 20% of all players, what should his minimum height be? What percent of all basketball players have their heights within two standard deviations of the average height?

Solution

Mean ( u ) =67
Standard Deviation ( sd )=3.89
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 72) = (72-67)/3.89
= 5/3.89 = 1.2853
= P ( Z >1.285) From Standard Normal Table
= 0.0993                  
around 9.93% are above 7

b)
P ( Z > x ) = 0.2
Value of z to the cumulative probability of 0.2 from normal table is 0.84
P( x-u/ (s.d) > x - 67/3.89) = 0.2
That is, ( x - 67/3.89) = 0.84
--> x = 0.84 * 3.89+67 = 70.2754                  

Minimum heoght should be 70.27

c)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
(67-2*3.89, 67+2*3.89)
=(59.22,74.78)