Chapter 11, Problem 20SGR

a.

To determine

To find the percent of players that have times between $4.6$ and $4.8$ seconds.

Answer to Problem 20SGR

  $54\%$

Explanation of Solution

Given:

The times in the $40$ meter dash for a selected group of professional football players those are normally distributed with mean $\mu =4.74$ secs, $\sigma =0.13$ secs.

Calculation:

Consider the times in the $40$ meter dash for a selected group of professional football players those are normally distributed with mean $\mu =4.74$ secs, $\sigma =0.13$ secs

Consider the random variable $X$ which is represent the times;

Consider the events

  $\begin{array}{l}4.6\le X\le 4.8\\ \frac{4.6-4.74}{0.13}\le \frac{X-4.74}{0.13}\le \frac{4.8-4.74}{0.13}\\ -1.08\le 0.46\end{array}$

Where $Z$ are the standard normal distributions.

Consider the probability:

  $P(4.6\le X\le 4.8)=P(-1.08\le 0.46)$

Calculate this using TI-83 calculator.

Step 1: Press 2^nd, VARS and Selects the DRAW;

  

Step 2: Press $1$ to select the Shade Norm and enter the lower and upper bound to calculate the probability;

  

Therefore,

  $\begin{array}{l}P(180\le X\le 490)=P(-1.83\le 0.10)\\ =0.54\end{array}$

Therefore $54\%$ of players have times between $4.6$ and $4.8$ seconds.

a.

To determine

To find the number of $800$ players that will have times below $4.5$ seconds.

Answer to Problem 20SGR

  $24$

Explanation of Solution

Given:

The times in the $40$ meter dash for a selected group of professional football players those are normally distributed with mean $\mu =4.74$ secs, $\sigma =0.13$ secs.

Calculation:

Consider the events:

  $\begin{array}{l}X\le 4.5\\ \frac{X-4.74}{0.13}\le \frac{4.5-4.74}{0.13}\\ Z\le -1.85\end{array}$

Where are the standard normal distributions.

Consider the probability:

  

  

Therefore,

  

Therefore, of players have times less than seconds.

As total number of players in the sample is therefore the number of players has times less than seconds is;

  

Therefore, the numbers of players have times less thanseconds is