Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 5 - Normal Probability Distributions - Review Exercises - Page 288: 49

Answer

The shortest braking distance of a sedan that can be in the top 10% is $131.88$ feet

Work Step by Step

A braking distance in the top 10% is any score above the 90th percentile. Thus, we have to find the z score that corresponds to the cumulative area 0.90. Using the standard normal table or technology we find that a z score of 1.28 corresponds to an area of 0.90. To find the corresponding $x$ value: z = $\frac{x - \mu}{\sigma}$ $x$ = $\mu$ + $z\sigma$ $x$ = $127 + (3.81 \times 1.28)$ $x$ = $131.88$ feet
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