Question

In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 41 mph and that the standard deviation was 16 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.

(a) Roughly what proportion of vehicle speeds were between 25 and 57 mph? (Round the answer to the nearest whole number.)
Approximately %

(b) Roughly what proportion of vehicle speeds exceeded 57 mph? (Round the answer to the nearest whole number.)
Approximately %

Answer 1

a. The proportion of vehicle speeds were between 25 and 57 mph is 68.26%

b.The proportion of vehicle speeds exceeded 57 mph is 15.87%.

Explanation:

a. To calculate what proportion of vehicle speeds were between 25 and 57 mph we would have to make the following calculations:

Probability that the vehicle speeds were between 25 and 57 mph is given by:

P(25≤x≤57)

=P(25-41 ≤ x-μ ≤ 57-41)

16 σ 16

=P(-1≤z≤1)

=P(z≤1)-P(z≤1)

=0.8413-0.1587

=0.6826

The proportion of vehicle speeds were between 25 and 57 mph is 68.26%

b. To calcuate what proportion of vehicle speeds exceeded 57 mph, we would have to make the following calculation:

Probability that vehicle speeds exceeded 57 mph is given by

P(x>57)

=P(x-μ > 57-41)

σ 16

=P(z>1)

=1-P(z≤1)

=1-0.8413

=0.1587

The proportion of vehicle speeds exceeded 57 mph is 15.87%.