Find and Interpret the Area under a Normal Curve
-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 460 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds.
A) 0.0107
B) 0.4893
C) 0.9893
D) 0.5107

Question

Quizplus · Accepted Answer

To find the probability, we calculate the z-score using the formula $z = \frac{X - \mu}{\sigma}$, where $X = 322$, $\mu = 460$, and $\sigma = 60$. This gives $z = \frac{322 - 460}{60} = -2.3$. Looking up -2.3 in the z-table gives us the probability of 0.0107, meaning there's a 1.07% chance a randomly selected boy can run the mile in less than 322 seconds.

Find and Interpret the Area Under a Normal Curve