n a study investigating the effect of car speed on accident severity, 5000 repor

Question

n 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 46 mph and that the standard deviation was 14 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 60 mph? (Round the answer to the nearest whole number.)
Approximately  %

(b) Roughly what proportion of vehicle speeds exceeded 60 mph? (Round the answer to the nearest whole number.)
Approximately  %

Explanation / Answer

Ans:

Given that

mean=46 and standard deviation=14

a)

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

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

P(-1<z<1)=P(z<1)-P(z<-1)

=0.8413-0.1587=0.6826 or 68% approximately

b)

z(60)=1

P(z>1)=01.587 or 16% approximately

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