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7.67 If X is the mean and s is the standard deviation of a set of normally distributed measurements, what percentage of the measurements are (a) within the range X ± 2s, (b) outside the range X ± 1.2s, and (c) greater than X - 1.5s? FL

7.67 If X is the mean and s is the standard deviation of a set of normally distributed measurements, what percentage of the measurements are (a) within the range X ± 2s, (b) outside the range X ± 1.2s, and (c) greater than X - 1.5s? FL

A First Course in Probability (10th Edition)
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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7.63 Adult males have normally distributed heights with mean equal to 70 in and standard deviation equal to 3 in. (a) What percent are shorter than 65 in? (b) What percent are taller than 72 in? (c) What percent are between 68 and 73 in? 7.64 The amount spent for goods online is normally distributed with mean equal to $125 and standard deviation equal to $25 for a certain age group. (a) What percent spend more than $175? (b) What percent spend between $100 and $150? (c) What percent spend less than $50? 7.65 The mean grade on a final examination was 72 and the standard deviation was 9. The top 10% of the students are to receive A's. What is the minimum grade that a student must get in order to receive an A? 7.66 If a set of measurements is normally distributed, what percentage of the measurements differ from the mean by (a) more than half the standard deviation and (b) less than three-quarters of the standard deviation? 7.67 If X is the mean and s is the standard deviation of a set of normally distributed measurements, what percentage of the measurements are (a) within the range X ± 2s, (b) outside the range X ± 1.2s, and (c) greater than X - 1.5s? 7.68 In Problem 7.67, find the constant a such that the percentage of the cases (a) within the range X ±as is 75% and (b) less than X - as is 22%.
Transcribed Image Text:7.63 Adult males have normally distributed heights with mean equal to 70 in and standard deviation equal to 3 in. (a) What percent are shorter than 65 in? (b) What percent are taller than 72 in? (c) What percent are between 68 and 73 in? 7.64 The amount spent for goods online is normally distributed with mean equal to $125 and standard deviation equal to $25 for a certain age group. (a) What percent spend more than $175? (b) What percent spend between $100 and $150? (c) What percent spend less than $50? 7.65 The mean grade on a final examination was 72 and the standard deviation was 9. The top 10% of the students are to receive A's. What is the minimum grade that a student must get in order to receive an A? 7.66 If a set of measurements is normally distributed, what percentage of the measurements differ from the mean by (a) more than half the standard deviation and (b) less than three-quarters of the standard deviation? 7.67 If X is the mean and s is the standard deviation of a set of normally distributed measurements, what percentage of the measurements are (a) within the range X ± 2s, (b) outside the range X ± 1.2s, and (c) greater than X - 1.5s? 7.68 In Problem 7.67, find the constant a such that the percentage of the cases (a) within the range X ±as is 75% and (b) less than X - as is 22%.
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