Question

Major league baseball game durations are normally distributed with a mean of 160 minutes and a standard deviation of 50 minutes. What is the probability of a game duration of between 180 and 210 minutes? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

Answer 1

0.19

Explanation:

μ = 160 and σ = 50. Find the z scores for 180 and 210.

z = (x - μ) / σ

z = (180 - 160) / 50 = 0.40

z = (210 - 160) / 50 = 1.00

So we want P(0.40<z<1.00). This can be found as:

P(0.40<z<1.00) = P(z<1.00) - P(z<0.40)

Now use a calculator or table to find each probability:

P(0.40<z<1.00) = 0.8413 - 0.6554

P(0.40<z<1.00) = 0.1859

Rounded to the nearest hundredth, P ≈ 0.19.