Question

A police officer gathered data on the speeds, in kilometres per hour (km/h), of some cars as they drove down hill towards her car. The speed limit is 50 km/h. Analysis of the results showed that the speeds of the cars were normally distributed with a mean speed of 56 km/h and a statndard deviation of 8 km/h.

" slow drivers" contribute to road rage problems and the officer noticed that 2 of the 150 drivers in her survey caused problems for other drivers beacuse of their slow speed. Use normal distrubution and this infomation to decribe a "slow" driver in terms of their driving.

thanks

Answer 1

I think I see what you are after here; I think you are trying to find the speed definition of "slow"

2 out of 150 is .0133. That is 1.33% of drivers are slow. Ergo, 1-.0133=.9866 are not slow. Look up .9866 in a normal distribution table (probably found in your stats book). I get 2.22. Meaning that 1.33% of the population are more than 2.22 standard deviations away from the mean (of a normally distributed population). So 8*2.22 = 17.76. And 56-17.76 = 38.24. Meaning, drivers going below 38.24 km/h are "slow drivers".

By the way, in my opinion, 150 drivers is too small of a sample size to determine the number of "slow" drivers. But this is an issue for another day.