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 46 mph and the standard deviation was 14 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.)

A) Approximately what percentage of vehicle speeds were between 32 and 60 mph?

B) Approximately what percentage of vehicle speeds exceeded 60 mph? (Round your answer to the nearest whole number.)

Answer 1

Given that, mean = 46 mph and standard deviation = 14 mph

According to Empirical rule,

approximately 68% of the data fall within 1 standard deviations of the mean.

A) For x = 32

z = (32 - 46) / 14 = -14/14 = -1

For x = 60

z = (60 - 46) / 14 = 14/14 = 1

Therefore, according to Empirical rule, approximately 68% of vehicle speeds were between 32 and 60 mph.

Answer : 68%

B) By Empirical rule, 100 - 68 = 32% of the data fall outside the 1 standard deviations of the mean. And 32/2 = 16% of the data fall below 1 standard deviations of the mean (i.e. 32 mph) and 16% of the data fall above 1 standard deviations of the mean (i.e. 60 mph).

Therefore, approximately 16% of vehicle speeds exceeded 60 mph.

Answer : 16%