Question

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5,000 fatal accidents. For these accidents, the mean speed was 46 mph and the standard deviation was 13 mph. A histogram revealed that the vehicle speed distribution was mound shaped and approximately symmetric. (Use the Empirical Rule.) (a) Approximately what percentage of vehicle speeds were between 33 and 59 mph

Answer 1

68%

Explanation:

Given that:

Mean speed (m) = 46

Standard deviation (s) = 13

Approximately what percentage of vehicle speeds were between 33 and 59 mph

Obtain the Zscore for P(Z < x) for both values and subtract :

For x = 33

Zscore :

Z = (x - m) / s

Z = (33 - 46) / 13 = - 1

p(Z < - 1) = 0.15866 ( Z probability calculator)

For x = 59

Zscore :

Z = (x - m) / s

Z = (59 - 46) / 13 = 1

p(Z < 1) = 0.84134 ( Z probability calculator)

Hence, 0.84134 - 0.15866 = 0.68268 = 0.68

0.68 * 100% = 68%