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The reading given by a thermometer calibrated in ice water

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 8SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 8SE

The reading given by a thermometer calibrated in ice water (actual temperature 0°C) is a random variable with probability density function

where k is a constant.

a. Find the value of k.

b. What is the probability that the thermometer reads above 0ºC?

c. What is the probability that the reading is within 0.25°C of the actual temperature?

d. What is the mean reading?

e. What is the median reading?

f. What is the standard deviation?

Step-by-Step Solution:

Answer

Step 1 of 6

a)Here we have to find the integration of the given pdf

   And that will be equal to total probability one

(1-⅓)-(-1+⅓) =1/k

             2-(⅔)=1/k

                   k=¾

                  k=0.75


Step 2 of 6

Chapter 2, Problem 8SE is Solved
Step 3 of 6

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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The reading given by a thermometer calibrated in ice water