Question

An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 15.00 and a standard deviation equal to 0.2 seconds. what percentage of players on the team run the 100-meter dash in 15.22 seconds or faster? (round your answer to two decimal places.)

Answer 1

0.8643 run the 100 meter dash in 15.22 seconds or faster.

We first compute the z-score for this time:

$z=\frac{X-\mu}{\sigma} \\ \\= \frac{15.22-15}{0.2}= \frac{0.22}{0.2}=1.1$

Using a z-table (http://www.z-table.com), we see the proportion of scores less than or equal to this is 0.8643.

Answer 2

Answer:

86.43 %

Step-by-step explanation:

Given,

Mean, $\mu$ = 15.00,

Standard deviation, $\sigma$ = 0.2 seconds,

By using the formula of z-score,

$z=\frac{x-\mu}{\sigma}$

The z-score for the data 15.22,

$z=\frac{15.22-15}{0.2}$  

$=\frac{0.22}{0.2}$

$=1.1$

Also, the player who takes less time is faster.

Thus, the percentage of players on the team run the 100-meter dash in 15.22 seconds or faster = P( z ≤ 1.1 ) = 0.8643 = 86.43 %    ( By z-score table )