percent finding with only mean and standard deviation

Question

An athletics coach states that the distribution of player run times for a 100-meter dash is normally distributed with a mean of 13.24 seconds and a standard deviation of .52 second. What percentage of players on the team run the 100-meter dash in 14 seconds or faster?

Answer 1

You can use the z-score formula to solve this problem:

z =(x-µ) / σ

x = raw score= 14 seconds

µ = mean = 13.24 seconds

σ = standard deviation = .52 seconds

z= (14-13.24)/.52

z= .76/.52 =1.4615

You can find a z-score calculator over the web or you can use the table to find 14 seconds and faster.

P(X≤14) = P(Z≤1.4615) ≈ 0.9281

The answer is 92.81%

*Note: The word faster might be a little tricky, which means less time.