Probabilities Using the Normal Distribution

The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage of pregnancies will last at least 300 days?

• 0.0164

• 0.9836

• 0.1234

• 0.5619

Answer explanation

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What percentage ratings can be expected to be between 200 and 275?

• 0.4331

• 0.5671

• 0.3861

• 0.2987

Answer explanation

In Standford, CA, cars were traveling at a mean speed of 23.84 mph, with a standard deviation of 3.56 mph. One car's z-score was +3.2. How fast was that car going?

• 72.728 mph

• 12.448 mph

• 35.232 mph

• 32.563 mph

Answer explanation

The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

• 0.4013

• 0.2403

• 0.5204

• 0.1407

For a recent English exam, the mean was 73 points and the standard deviation was 9.2 points. Find the percent of scores over 85.

• 0.0961

• 0.9039

• 0.2851

• 0.7531

For a recent English exam, the mean was 73 points and the standard deviation was 9.2 points. Find the percent of scores under 58.

• 0.9485

• 0.0515

• 0.6521

• 0.5531

A town has a speed limit of 45 mph. If the speeds of cars traveling in the town can be described by a Normal model with a mean of 48 mph and a standard deviation of 3.5 mph, what percent of cars are exceeding the speed limit?

• 80.43%

• 19.56%

• 23.86%

• 75%

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what percent of snowfall amounts will be between 40 and 50?

• 0.5393

• 0.4607

• 0.3719

• 0.7234

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915
• 0.1762
• 0.8238
• -0.93

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%
• 47.5%
• 68%
• 95%