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.

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.

MathGuru · Answer

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.

Anonymous · Answer

.4987 .4988