Suppose that the distance of fly balls threw (hit) to the outfield (in baseball) is normally distributed with a mean of 246 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball. Round all answers to two decimal places.

A. X ~ N( , )
B. Find the probability that a randomly hit fly ball travels less than 200 feet.
C. Find the 70th percentile for the distribution of fly balls.

a)

b) 0.1191

c)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 246 feet

Standard Deviation, σ = 39 feet

We are given that the distribution of distance of fly balls is a bell shaped distribution that is a normal distribution.

a) Distribution of X

Let X be the distance in feet for a fly ball. Then,

b) Probability that a randomly hit fly ball travels less than 200 feet.

Calculation the value from standard normal z table, we have,  

c) 70th percentile for the distribution of fly balls.

We have to find the value of x such that the probability is 0.7

Calculation the value from standard normal z table, we have,  

The 70th percentile for the distribution of fly ball is 266.44 feet.

answer: x=60