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. Find the probability that a randomly selected boy in secondary school will take longer than 335 seconds to run the mile. A) 0.5107 B) 0.9893 C) 0.0107 D) 0.4893

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 = 450Standard Deviation, σ = 50We 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 0.10P(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.