A physical fitness association is including the mile run in its secondary-school fitness test. The time for thisevent for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and astandard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school willtake longer than 302 seconds to run the mile.
A) 0.9893
B) 0.4893
C) 0.0107
D) 0.5107

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected boy takes longer than 302 seconds, we calculate the Z-score for 302 seconds and then find the corresponding probability. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is 302 seconds, $\mu$ is 440 seconds, and $\sigma$ is 60 seconds. This gives us a Z-score of $\frac{302 - 440}{60} = -2.3$. Looking up this Z-score in a standard normal distribution table or using a calculator, we find that the probability of a score being less than -2.3 is approximately 0.0107. Since we want the probability of taking longer than 302 seconds, we subtract this from 1, giving us $1 - 0.0107 = 0.9893$.

A Physical Fitness Association Is Including the Mile Run in Its