Question

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? (8 pts)

Answer 1

Answer:

The boys need to complete the run in 385.9 seconds or less in order to earn a certificate of recognition from the fitness association.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 450

Standard Deviation, σ = 50

We are given that the distribution of time for fitness test is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.10

P(X<x) = 0.10

$P( X < x) = P( z < \displaystyle\frac{x - 450}{50})= 0.10$

Calculation the value from standard normal z table, we have,  

$P(z\leq -1.282) = 0.10$

$\displaystyle\frac{x - 450}{50} = -1.282\\\\x = 385.9$

Hence, boys need to complete the run in 385.9 seconds or less in order to earn a certificate of recognition from the fitness association.