The time it takes a runner of a marathon in a certain city to fifinish the race (fifinish time) has a distribution that can be approximated by a Normal distribution with a mean of 195 minutes and a standard deviation of 25 minutes. The faster 2.5% classify automatically for next year’s marathon. What fifinish time qualififies athletes automatically for the next marathon?( faster means lowest 2.5%)

The time it takes a runner of a marathon in a certain city to fifinish the race (fifinish time) has a distribution that can be approximated by a Normal distribution with a mean of 195 minutes and a standard deviation of 25 minutes. The faster 2.5% classify automatically for next year’s marathon. What fifinish time qualififies athletes automatically for the next marathon?( faster means lowest 2.5%)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The time it takes a runner of a marathon in a certain city to fifinish

the race (fifinish time) has a distribution that can be approximated by

a Normal distribution with a mean of 195 minutes and a standard

deviation of 25 minutes. The faster 2.5% classify automatically for next

year’s marathon. What fifinish time qualififies athletes automatically for

the next marathon?( faster means lowest 2.5%)

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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