Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 263 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N( ? , ? ) b. Find the probability that a randomly hit fly ball travels less than 284 feet. ? Round to 4 decimal places. c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ?

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 263 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N( ? , ? ) b. Find the probability that a randomly hit fly ball travels less than 284 feet. ? Round to 4 decimal places. c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ?

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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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 263 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball.

a. What is the distribution of X? X ~ N( ? , ? )

b. Find the probability that a randomly hit fly ball travels less than 284 feet. ? Round to 4 decimal places.

c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ? feet

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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