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Dead battery? A car company has found that the lifetime of its batteries varies from car

The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor ISBN: 9781464108730 488

Solution for problem 54 Chapter 7.3

The Practice of Statistics | 5th Edition

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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor

The Practice of Statistics | 5th Edition

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Problem 54

Dead battery? A car company has found that the lifetime of its batteries varies from car to car according to a Normal distribution with mean m = 48 months and standard deviation s = 8.2 months. The company installs a new brand of battery on an SRS of 8 cars. (a) If the new brand has the same lifetime distribution as the previous type of battery, describe the sampling distribution of the mean lifetime x . (b) The average life of the batteries on these 8 cars turns out to be x = 42.2 months. Find the probability that the sample mean lifetime is 42.2 months or less if the lifetime distribution is unchanged. What conclusion would you draw?

Step-by-Step Solution:

Step 1 of 3

Consider that X be the lifetime of batteries following normal distribution with mean  and standard deviation  

 

Step 2 of 3

Chapter 7.3, Problem 54 is Solved
Step 3 of 3

Textbook: The Practice of Statistics
Edition: 5
Author: Daren S. Starnes, Josh Tabor
ISBN: 9781464108730

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Dead battery? A car company has found that the lifetime of its batteries varies from car