The time to run a mile is normally distributed with a mean time of 9 minutes and a standard deviation of 1.7 minutes. If someone wanted to be in the top 10% of runners, what time would then need to run it in?
To find the time needed to be in the top 10% of runners, we need to find the z-score corresponding to the top 10% of the normal distribution.
Since the top 10% is being considered, we should look for the z-score that corresponds to a cumulative probability of 0.90. Consulting a standard normal distribution table or using a calculator, we find that the z-score is approximately 1.28.
We can use the formula for z-score to find the corresponding time:
z = (x - μ) / σ
Rearranging the formula, we have:
x = z*σ + μ
Substituting in the given values, we get:
x = 1.28 * 1.7 + 9
Calculating this equation, we find:
x ≈ 1.25 + 9 ≈ 10.25
Therefore, to be in the top 10% of runners, someone would need to run the mile in approximately 10.25 minutes.