Suppose that the distance of fly balls hit to the outfield i

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 229 feet and a standard deviation of 52 feet. We randomly sample 64 fly balls.

Let X= average distance in feet for 64 fly balls. Enter numbers as integers or fractions in \"p/q\" form, or as decimals accurate to nearest 0.01 .

Use the mean and standard deviation of X to determine the z value for X=240 . z= .

What is the probability that the 64 balls traveled an average of greater than 240 feet? P(X>240)=

Find the 80th percentile of the distribution of the average of 64 fly balls. That is, find x so that P(X

Solution

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 229 feet and a standard deviation of 52 feet. We randomly sample 64 fly balls.

Let X= average distance in feet for 64 fly balls. Enter numbers as integers or fractions in \"p/q\" form, or as decimals accurate to nearest 0.01 .

Use the mean and standard deviation of X to determine the z value for X=240 . z= .

Mean =229

standard deviation of X = 52/sqrt(64) =6.5

z=(240-229)/6.5 =1.69

What is the probability that the 64 balls traveled an average of greater than 240 feet? P(X>240)=

P( mean X>240)=

=P( z >1.69) = 0.0455

Find the 80th percentile of the distribution of the average of 64 fly balls.

Z value for 80^th percentile =0.842

X value =229+0.842*6.5 = 234.473

Required value =234.47 ( 2 decimals).