You are the coach of a basketball team that is currently loo

You are the coach of a basketball team that is currently looking for new players. One of the criteria for selection as a player is that the person must be above a particular height. Ideally, you want your next player to be as tall as possible. However, you do not want to rule out any potential players by making the cut-off height too strict.

You decide that accepting players within the top 2.5% height bracket will be reasonable for your team. Assume that the height of all people follows a normal distribution with a mean of 71.6 in and a standard deviation of 2.8 in.

Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team. You may find this standard normal table useful. Give your answer in inches to the nearest inch.

C =

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.975      
          
Then, using table or technology,          
          
z =    1.959963985      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    71.6      
z = the critical z score =    1.959963985      
s = standard deviation =    2.8      
          
Then          
          
x = critical value =    77.08789916 = 77 in   [ANSWER, cut off height]