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 440 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 302 seconds.
A).5107
B).9893
C).4893
D).0107

Question

Quizplus · Accepted Answer

To find the probability, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question (302 seconds), μ is the mean (440 seconds), and σ is the standard deviation (60 seconds). Plugging in the values, we get Z = (302 - 440) / 60 = -138 / 60 = -2.3. Looking up the Z-score of -2.3 in a standard normal distribution table gives us a probability of approximately 0.0107. This means there's a 1.07% chance a randomly selected boy can run the mile in less than 302 seconds.

A Physical Fitness Association Is Including the Mile Run in Its