Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 236 feet and a standard deviation of 44 feet. We randomly sample 49 fly balls.Part (a)If X =average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places.X ____, ________,_______ ~ .Part (b)What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Part (c)Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.) ft†

Answered: Suppose that the distance of fly balls…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 236 feet and a standard deviation of 44 feet. We randomly sample 49 fly balls.

Part (a)

If X =average distance in feet for 49 fly balls, then give the distribution of
X.
Round your standard deviation to two decimal places.

X ____, ________,_______
~

.
Part (b)

What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)

Sketch the graph. Scale the horizontal axis for
X.
Shade the region corresponding to the probability.
Part (c)

Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)
ft

†

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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