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Life Spans of Tires A certain brand of automobile tire has

Elementary Statistics: Picturing the World | 6th Edition | ISBN: 9780321911216 | Authors: Ron Larson; Betsy Farber ISBN: 9780321911216 66

Solution for problem 47E Chapter 2.5

Elementary Statistics: Picturing the World | 6th Edition

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Elementary Statistics: Picturing the World | 6th Edition | ISBN: 9780321911216 | Authors: Ron Larson; Betsy Farber

Elementary Statistics: Picturing the World | 6th Edition

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Problem 47E

Problem 47E

Life Spans of Tires A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.

(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.

(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Step-by-Step Solution:

Solution :

Step 1 of 2:

Given a certain brand of automobile tire has a mean lifespan of 35,000 miles and a standard deviation of 2250 miles.

Here  and .

Our goal is :

a). We need to find the z-score that corresponds to each life span.

b). We need to find the percentile that corresponds to each life span.

a). Given the life spans of 3 randomly selected tires :

34,000 miles, 37,000 miles, and 30,000 miles.

The z-score formula is

z =

The life span of 34,000 days is

z =

We know that  and .

z =

z =

z = -0.4444

Therefore, the z-score is -0.4444.

The life span of 37,000 days is

z =

We know that  and .

z =

z =

z = 0.8888

Therefore, the z-score is 0.8888.

The lifespan of 30,000 days is

z =

We know that  and .

z =

z =

z = -2.2222

Therefore, the z-score is -2.2222.

Hence, the z-score is -2.22, has an unusual life span.


Step 2 of 2

Chapter 2.5, Problem 47E is Solved
Textbook: Elementary Statistics: Picturing the World
Edition: 6
Author: Ron Larson; Betsy Farber
ISBN: 9780321911216

Elementary Statistics: Picturing the World was written by and is associated to the ISBN: 9780321911216. Since the solution to 47E from 2.5 chapter was answered, more than 605 students have viewed the full step-by-step answer. This full solution covers the following key subjects: life, spans, tires, span, selected. This expansive textbook survival guide covers 66 chapters, and 3049 solutions. This textbook survival guide was created for the textbook: Elementary Statistics: Picturing the World , edition: 6. The answer to “Life Spans of Tires A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.________________(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.” is broken down into a number of easy to follow steps, and 99 words. The full step-by-step solution to problem: 47E from chapter: 2.5 was answered by , our top Statistics solution expert on 08/25/17, 09:43AM.

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