Solve the problem.
-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) 0.4893
B) 0.5107
C) 0.0107
D) 0.9893

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly selected boy can run a mile in less than 302 seconds.

Using the formula for z-score:

z = (x - μ) / σ

where x is the value we want to find the probability for (302 seconds in this case), μ is the mean (440 seconds), and σ is the standard deviation (60 seconds).

Substituting the values:

z = (302 - 440) / 60 = -2.267

Using a standard normal distribution table (or calculator), we can find the probability corresponding to this z-score:

P(z < -2.267) = 0.0107

Therefore, the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds is 0.0107, which corresponds to answer choice C.

Solve the Problem. -A Physical Fitness Association Is Including the Mile Run in Mile