Question

A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school players’ weights are normally distributed and that this year, the mean weight is 225 pounds with a standard deviation of 43 pounds. Calculate the weight at which the coach should start recruiting players.

Answer 1

Answer:

The coach should start recruiting players with weight 269.55 pounds or more.                                                    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 225 pounds

Standard Deviation, σ = 43 pounds

We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.15

$P( X > x) = P( z > \displaystyle\frac{x - 225}{43})=0.15$  

$= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15$  

$=P( z \leq \displaystyle\frac{x - 225}{43})=0.85$  

Calculation the value from standard normal z table, we have,  

$P(z < 1.036) = 0.85$

$\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55$

Thus, the coach should start recruiting players with weight 269.55 pounds or more.