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 450 seconds and a
Standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school will
Take longer than 312 seconds to run the mile.
A) 0.0107
B) 0.9893
C) 0.5107
D) 0.4893

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected boy will take longer than 312 seconds to run the mile, we first calculate the Z-score for 312 seconds using the formula Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Substituting the given values, we get Z = (312 - 450) / 60 = -138 / 60 = -2.3. Looking up the Z-score of -2.3 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're interested in the probability of taking longer than 312 seconds, we subtract this value from 1 (because the total probability is 1). Therefore, 1 - 0.0107 = 0.9893, which means there's a 98.93% chance a randomly selected boy will take longer than 312 seconds to run the mile.

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