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 48 mph and the standard deviation was 16 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 32 and 64 mph

Answer 1

Answer:

68%

Step-by-step explanation:

The Empirical rule formula =

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

mean speed was 48 mph and the standard deviation was 16 mph.

Testing out the first rule in Empirical rule

= 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

μ - σ

= 48 - 16

= 32

μ + σ

= 48 + 16

= 64

From the above use of the empirical rule,we can see that 68% of the data falls in 32mph

And 68% of the data falls in 64 mph

Hence , 68% + 68% /2

= 136%/2

= 68%

Therefore, the approximate percentage of vehicle speeds that were between 32 and 64 mph is 68%