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Statistics / Probability and Statistics for Engineers and the Scientists 9 / Chapter 6 / Problem 6.20

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

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Solved: The weights of a large number of miniature poodles

Chapter 6, Problem 6.20

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QUESTION:

The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram, find the fraction of these poodles with weights

(a) over 9.5 kilograms;

(b) of at most 8.6 kilograms;

(c) between 7.3 and 9.1 kilograms inclusive.

Questions & Answers

QUESTION:

The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram, find the fraction of these poodles with weights

(a) over 9.5 kilograms;

(b) of at most 8.6 kilograms;

(c) between 7.3 and 9.1 kilograms inclusive.

ANSWER:

Step 1 of 4

Given:

Mean weight (\(\mu \)) of miniature poodles = 8 kilograms

Standard deviation (\(\sigma \)) of weight = 0.9 kilograms

Measurements are recorded to the nearest tenth of a kilogram, which means we are dealing with a continuous random variable.

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