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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.)

Respuesta :

Answer:

86.43 %

Step-by-step explanation:

Given,

Mean, [tex]\mu[/tex] = 15.00,

Standard deviation, [tex]\sigma[/tex] = 0.2 seconds,

By using the formula of z-score,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

The z-score for the data 15.22,

[tex]z=\frac{15.22-15}{0.2}[/tex]  

[tex]=\frac{0.22}{0.2}[/tex]

[tex]=1.1[/tex]

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 )

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