Question

The National Highway Traffic Safety Administration analyzes the crash test data for new cars. One variable measured is the severity of the injury due to a collision. The higher the severity, the higher the points assigned. Assume that the injury rating is normally distributed with a mean (μ) of 605 points and a standard deviation (σ) of 185 points. One of the crash-test cars is randomly selected from the data and its rating is observed.
Find the probability that the rating will fall between 500 and 700 points.

Answer 1

Use z-scores.

Formula:

z = (x - mean)/sd

Find two z-scores, using 500 for x and also 700 for x. Mean = 605 and sd = 185.

Once you find the two z-scores, use a z-distribution table to determine your probability between the two z-scores.

Answer 2

.4987
.4988