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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X<x) = 0.10
[tex]P( X < x) = P( z < \displaystyle\frac{x - 450}{50})= 0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z\leq -1.282) = 0.10[/tex]
[tex]\displaystyle\frac{x - 450}{50} = -1.282\\\\x = 385.9[/tex]
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.
