Answer:
66 minutes
Step-by-step explanation:
Let X be the running time of a contestant in the race.
Given that the running times are normally distributed, with a mean (μ) of 61 min and a standard deviation (σ) of 5 min, then:
X ~ N(61, 5²)
To find the qualifying time for the race, we need to determine the running time that corresponds to the top 16% of all applicants, so we need to find the value of a for the following:
P(X ≥ a) = 0.16
P(X ≤ a) = 1 - 0.16 = 0.84
Input the following in the inverse normal function on a calculator:
Therefore:
a = 65.9722855... = 66
So:
P(X ≥ 66) ≈ 0.16
Therefore, the qualifying time for the race to the nearest minute is approximately 66 minutes.