Chapter 2.2, Problem 54E

To determine

Percentage of players that are at risk of sitting on the bench during important games.

Answer to Problem 54E

Around 3.67% of the players have risk of sitting on the bench during important games.

Explanation of Solution

Given information:

Batting average value, $x=0.200$

Mean, $\mu =0.261$

Standard deviation, $\sigma =0.034$

Calculations:

Calculate the Z − score,

  $z=\frac{x-\mu }{\sigma }=\frac{0.200-0.261}{0.034}\approx -1.79$

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with -1.7 and the column that starts with .09 of the standard normal probability table for $P\left(z<-1.79\right)$ .

  $\begin{array}{l}P\left(x<0.200\right)=P\left(z<-1.79\right)\\ =1-P\left(z>-1.79\right)\\ =1-0.9633\\ =0.0367\\ =3.67\%\end{array}$

Therefore,

Around 3.67% of the players have batting average below 0.200 and are at risk of sitting on the bench during important games.