Question

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 70.3 in and a standard deviation of 2.1 in. Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team. Give your answer in inches to the nearest inch.C = ______ in

Answer 1

Answer:

The  value is  $x = 74.416 \ in$

Step-by-step explanation:

From the question we are told that

    The mean is  $\mu = 70.3\ in$

     The standard deviation is  $\sigma = 2.1\ in$

   

Generally the probability of  getting people with height  in the top 2.5% is mathematically represented as

  $P(X > x ) = P(\frac{X - \mu }{\sigma} > \frac{x - 70.3 }{2.1 } ) = 0.025$

Generally    

         $\frac{X - \mu }{\sigma} = Z (The \ standardized \ value \ of X )$

=>    $P(X > x ) = P(Z > \frac{x - 70.3 }{2.1 } ) = 0.025$

Generally the critical  value of  0.025 from the normal distribution table is  

      $Z_{0.025} = 1.96$

So

      $\frac{x - 70.3 }{2.1 } = 1.96$

=>   $x = 74.416 \ in$