The proportion of traffic fatalities resulting from drivers

The proportion of traffic fatalities resulting from drivers with high school blood levels in 1982 was approximately normally distributed among U.S. states, with mean 0.569 and standard deviation 0.068 (U.S. Department of Transportation Traffic Safety Facts 1999).

a. What proportion of states would you expect to have more than 65% of their traffic fatalities from drunk driving?

b. What proportion of deaths due to drunk driving would you expect to be at the 25th percentile of this distribution?

Solution

a. z= (.65-.569)/0.068= 1.19

Looking at a normal curve table we find that 0.883 are below a z score of 1.19 so (1-.883) or 0.117 would be above, so 0.117 would be the proportion.

b.-0.674 is the z score for the 25% percentile (from normal curve table) so

-0.674= (x-.569)/0.068

0.523 would be expected to be this proportion