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 48 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 32 and 64 mph? (Round the answer to the nearest whole number.)
Approximately   %

(b) Roughly what proportion of vehicle speeds exceeded 64 mph? (Round the answer to the nearest whole number.)
Approximately   %

Answer 1

Given :-

Part a)  Roughly what proportion of vehicle speeds were between 32 and 64 mph?

P ( 32 < X < 64 )

Standardizing the value

P ( 32 < X < 64 ) = P ( -1 < Z < 1)

= P ( Z < 1 ) - P ( Z < -1 )

= 0.8413 - 0.1587

P ( 32 < X < 64 ) = 0.6827

To find the precentage   0.6827 * 100 = 68.27%   68 %

Part b)   Roughly what proportion of vehicle speeds exceeded 64 mph?

P ( X > 64 ) = 1 - P ( X < 64 )

= 1 - P ( Z < 1 )

= 1 - 0.8413

P ( X > 64 ) = 0.1587

To find the precentage  0.1587 * 100 = 15.87 %   16%