Chapter 12, Problem 28SGR

a.

To determine

Find the percent of players have times below $4.4$ .

Answer to Problem 28SGR

  $2.5\%$

Explanation of Solution

Given information:

The time in the $40meter$ dash of football players is normally distributed with a mean of $4.7$ and standard deviation of $0.15$ .

Calculation:

Consider the figure,

  

The percent of players have times below $4.4$ is $2.5\%$ .

b.

To determine

Find the number of players have time between $4.55and4.85$ out of $800$ players.

Answer to Problem 28SGR

  $544$

Explanation of Solution

Given information:

The time in the $40meter$ dash of football players is normally distributed with a mean of $4.7$ and standard deviation of $0.15$ .

Calculation:

Consider the figure,

  

  $\begin{array}{l}4.55=4.7-\left(0.15\right)\\ =\mu -\sigma \\ 4.85=4.7+0.15\\ =\mu +\sigma \end{array}$

The probability the players has time between $4.55and4.85$

  $\begin{array}{l}P\left(\mu -\sigma <X<\mu +\sigma \right)=P\left(4.55<X<4.85\right)\\ =Grayshadedregion\\ =34\%+34\%\\ =68\%\end{array}$

Number of player out of $800$ have time between $4.55and4.85$ ,

  $\begin{array}{l}68\%of800\\ \frac{68}{100}\times 800\\ =544\end{array}$

Hence, the number of players have time between $4.55and4.85$ out of $800$ players are $544$ .