Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 254 feet and a standard deviation of 42 feet. We randomly sample 49 fly balls.

a. If ^-X = average distance in feet for 49 fly balls, then give the distribution of ^-X ~ ? (?,?) -ANSWER THE ?

b. What is the probability that the 49 balls traveled an average of less than 246 feet? (Round your answer to four decimal places.)

c. Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)
______ft

Answer 1

Solution :

Given that ,

mean = = 254

standard deviation = = 42

n = 49

= 254

= / n = 42 / 7 = 42 / 7 = 6

(a)

~ N(254 , 6)

(b)

P( < 246) = P(( - ) / < (246 - 254) / 6)

= P(z < -1.33)

= 00918

(c)

P(Z < 0.84) = 080

z = 0.84

Using z-score formula,

= z * + = 0.84 * 6 + 254 = 259.04

80th percentile = 259..04 ft