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

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 7 ft =   84 in      
u = mean = 6\' 7\" =    79 in      
          
s = standard deviation =    3.89 in      
          
Thus,          
          
z = (x - u) / s =    1.285347044      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.285347044   ) =    0.099335519 [ANSWER]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1-0.20 =    0.8      
          
Then, using table or technology,          
          
z =    0.841621234      
          
As x = u + z * s,          
          
where          
          
u = mean =    79      
z = the critical z score =    0.841621234      
s = standard deviation =    3.89      
          
Then          
          
x = critical value =    82.2739066 in [ANSWER]      
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c)

By empirical rule, this is 95.45%. [ANSWER]