Statistics and Probability

Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 42 feet. Let X = distance in feet for a fly ball.

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet? (Round your answer to four decimal places.)

Answer 1

Hello, thank you for taking the time to post your question!

The process on this type of question is to start by computing the Z score using the formula Z = (x – mean) / (standard deviation), then once you have that value you can convert it over to a probability using either technology like Excel or a normal distribution table.

When I do that process for this one I get Z = (216 – 250) / 42 = -34/42 = -0.81

Converting that over to a probability using a calculator gives me 0.2091 for the end probability value rounded to 4 decimal places.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)