Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 210 feet and a standard deviation of 40 feet. Let X = distance in feet for a fly ball.

A) Give the distribution of X.

X ~ __ ____,_____

B) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 184 feet? (Round your answer to four decimal places.)

c) Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.) in feet

Answer 1

solution:

Given data is

Normally distributed with a mean of 210 feet and a standard deviation of 40 feet. Let X = distance in feet for a fly ball.

a) The distribution of X

The distribution for x is normal distribution with mean 210

and

standard deviation = 40

b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 184 feet.

The probability that this ball traveled fewer than 184 feet is 0.257846.

x=184

By applying normal distribution:-

= - 0.65

z = -0.65

p ( z < - 0.65 ) = 0.257846

c) The 80th percentile of the distribution of fly balls.

80th percentile of the distribution of fly balls is 243.8

p-value for the 80th percentile=0.80

z-score for the p-value(0.80)=0.845

By applying normal distribution:-

x=243.8