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 450 seconds and astandard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school canrun the mile in less than 335 seconds.
A) 0.0107
B) 0.4893
C) 0.9893
D) 0.5107

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected boy can run the mile in less than 335 seconds, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (335 seconds), $\mu$ is the mean (450 seconds), and $\sigma$ is the standard deviation (50 seconds). Plugging in the values, we get $Z = \frac{335 - 450}{50} = -2.3$. Looking up -2.3 on the standard normal distribution table gives us a probability of approximately 0.0107.

A Physical Fitness Association Is Including the Mile Run in Its