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 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?

b. Roughly what proportion of vehicle speeds exceeded 57 mph?

(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) Roughly 16% of vehicle speeds exceeded 57 mph.

Step-by-step explanation:

We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.

For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.

Let X = vehicle speed at impact

SO, X ~ Normal()

Here, = population average speed = 42 mph

          = standard deviation = 15 mph

Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;

(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;

68% data values will lie between [ ] , i.e;

        [ ]  =  [42 + 15 , 42 - 15]

                                 =  [57 , 27]

So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.

It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.

This means that roughly 16% of vehicle speeds exceeded 57 mph.

x= 149. 24+7=31. 180-31=149

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