In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 43 mph and the standard deviation was 17 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.) (a) Approximately what percentage of these vehicle speeds were between 26 and 60 mph?

In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 43 mph and the standard deviation was 17 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.) (a) Approximately what percentage of these vehicle speeds were between 26 and 60 mph?

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 43 mph and the standard deviation was 17 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.)
(a)
Approximately what percentage of these vehicle speeds were between 26 and 60 mph?

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Expert Solution

Step 1

Given n = 5000, $μ = 43 a n d σ = 17$

Using standard normal,

$Z = \frac{X - μ}{σ} ~ N (0, 1)$

$P (26 < X < 60) = P (\frac{26 - 43}{17} < Z < \frac{60 - 43}{17})$

= $P (- 1 < Z < 1)$

= $1 - P (Z < 1)$

= 1- 0.8413 (from standard normal table)

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