Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 252 feet and a standard deviation of 51 feet.

Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 192 feet?
(fewer than 192 feet) =
%
b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled more than 204 feet?
(more than 204 feet) =

Answer 1

The probability that the balled traveled fewer than 192 feets and more than 204 feets are 12.0% and 82.7% respectively.

Using the parameters given ;

• Mean = 252 feets
• standard deviation = 51 feets

Firstly, we need to calculate the Zscore which corresponds to the given score

Zscore = (Score - Mean) / standard deviation

Now we have;

A.)

For fewer than 192 feets

Zscore = (192 - 252) / 51

Zscore = -1.176

Using the normal distribution table ; the probability for the zscore obtained is ;

P(Z < -1.176) = 0.1198 ≈ 12.0%

b.)

For more than 204 feets

Zscore = (204 - 252) / 51

Zscore = -0.941

Using the normal distribution table ; the probability for the zscore obtained is ;

P(Z > -0.941) = 0.8267 ≈ 82.7%