Please answer the problem. also I believe for the second box in part a is suppos

Question

Please answer the problem. also I believe for the second box in part a is supposed to contain a z square value of the standard deviation and NOT the regular deviation

thlynx.com/online/collab stat clt eval cum?mode eval&course; id-71 Problem 2 Suppose that the distance of fty balls hit to the outfield (in baseball) ?s normalty distributed with a mean of 245 feet and a standard deviation of 44 feet. We randomly sample 56 fly balls. Let X- average distance in feet for 56 fly balls Enter numbers as integers or fractions in "p/q" form, or as decimals accurate to nearest 0.01 a. (20) X (pick one)v b. (20) Use the mean and standard deviation of I to determine the a value for X 240 c (20) Mustrate P(X 240) as an area by adjusting the slider along the horizontal axis to control the value ?. 000 0.300 0.2 0 1 Fill left OFillright d (20) What is the probability that the 56 balls traveled an average of greater than 240 feet? P(x 240) e. (20) Find the 80th percentile of the distribution of the average of 56 thy balls That is, find so that Px) 0.8 Type here to search 851 PM 3/26/2018

Explanation / Answer

Solution:-
a) X-bar ~ N (245 , 44/sqrt(56))

b) n = 56, X-bar = 240

Z = (X-bar - mean)/(sd/sqrt(n))
= (240 - 245)/(44/sqrt(56))
= -0.8504

c) P(X-bar > 240) = P(Z > -0.8504)
= 0.8023

d) P(X-bar < x) < 0.80

(x - mean)/(s/sqrt(n)) = Z

(x - 245)/5.8797 = 0.8416

x = 245 + (0.8416*5.8797)

x = 249.9483

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