Question

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5000 fatal accidents. For these accidents, the mean speed was 42 miles per hour with a standard deviation of 15 miles per hour. Assuming the speeds are normally distributed, use the empirical rule to answer the following: a) About what percent of vehicle speeds were between 42 and 72 miles per hour? b) About what percent of vehicle speeds were in excess of 57 miles per hour? c) About what percent of vehicle speeds were below 12 miles per hour? d) About what percent of vehicle speeds were between 12 miles per hour and 57 miles per hour?

Answer 1

(a)

= 42

= 15

To find P(42 < X < 72):

Z = (72 - 42)/15

= 2.0

By empirical rule, area = 0.9545/2 = 0.4773 = 47.73%

So,

Answer is:

47.73 %

(b)

= 42

= 15

To find P(X>57):

Z = (57 - 42)/15

= 1;0

By empirical rule, area = (0.50- 0.3413) = 0.1587 = 15.87%

So,

Answer is:

15.87 %

(c)

= 42

= 15

To find P(X<12)"

Z = (12 - 42)/15

= - 2.0

By empirical rule, area = 0.5 - 0.9545/2 = 0.5 - 0.4773= 2.27%

So,

Answer is:

2.27 %

(d)

= 42

= 15

To find P(12 < X < 57):

For X= 12:

Z = (12 - 42)/15

= - 2.0

By empirical rule, area = 0.9545/2 = 0.4773

For X = 57:

Z = (57 - 42)/15

= 1.0

By empirical rule, area = 0.3413

So,

P(12 < X < 57):= 0.4773 + 0.3413 = 0.8184 = 81.84%

Answer is:

81.84 %