Question

A study conducted under the auspices of the National Highway Traffic Safety Administration found that the average number of fatal crashes caused by the drowsy drivers each year was 1550 (Business Week, January 26, 2015). Assume the annual number of fatal crashes per year is normally distributed with a standard deviation of 300 and mean of 1550.

For a year to be in the top 2.5 % of the distribution with respect to the number of fatal crashes, how many fatal crashes would have to occur?

Answer 1

Average number of crashed = µ = 1550,

Standard deviation σ = 300

To be in the top 2.5%, P(z) = 97.5%

From the z table, z = 1.96 for P(z) = 97.5%

Let the number of crashed be x

z = (x - µ) / σ

=> 1.96 = (x - 1550) / 300

=> x = 1550 + 1.96*300 = 2138

Hence, for the year to be in top 2.5% of the distribution, there should be a minimum of 2138 crashed in the year