23 The proportion of traffic fatalities resulting from drive

23. The proportion of traffic fatalities resulting from drivers with high alcohol 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? Q23

Solution

Normal with mean = 0.569 and sigma = 0.068

P >0.65 means z = 1.04

i.e. x >0.569+0.068(1.04)

x =0.640

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25th percentile for z = 0.675

x = 0.569+0.068(0.675)

= 0.6149