As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 60 minutes and standard deviation 9 minutes. a. Determine the percentage of finishers who have times between 55 and 75 minutes. b. Obtain and interpret the 70th percentile for the finishing times. c. Find the middle 60% of the finishing times.

As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 60 minutes and standard deviation 9 minutes. a. Determine the percentage of finishers who have times between 55 and 75 minutes. b. Obtain and interpret the 70th percentile for the finishing times. c. Find the middle 60% of the finishing times.

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

As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 60 minutes and standard deviation 9 minutes.
a. Determine the percentage of finishers who have times between 55 and 75 minutes.
b. Obtain and interpret the 70th percentile for the finishing times.
c. Find the middle 60% of the finishing times.

d. If a random sample of 15 Runner’s are selected find the probability that their mean finishing time is between 55 and 75 minutes.

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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