Probability Under the Normal Distribution

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 of ratings can be expected to be between 200 and 275?

• 0.4331

• 0.5671

• 0.3861

• 0.2987

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

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

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what values should border the middle 50% snowfalls?

• 44 and 52 inches

• 42 and 54 inches

• 40 and 50 inches

• 40 and 60 inches

This data is normally distributed.  What percent of the data is in the shaded region?

• 68%

• 95%

• 99.7%

• 50%

This data is normally distributed.  What percent of the data is in the shaded region?

• 68%

• 95%

• 99.7%

• 50%

This data is normally distributed. If this histogram represents data from 500 people, HOW MANY people are within two standard deviations of the mean?

• 499

• 475

• 340

• 47500

Answer explanation

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. For 500 people, this means about 475 people are within this range, making 475 the correct answer.

Abigail is analyzing the test scores of her class, which are normally distributed. What percent of the scores fall within the shaded region?

• 68%

• 95%

• 99.7%

• 50%

Abigail collected data on the heights of 500 students in her school, and the data is normally distributed. HOW MANY students are within two standard deviations of the mean height?

• 499

• 475

• 340

• 47500

Answer explanation

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. For 500 people, this means about 475 people are within this range, making 475 the correct answer.

What percent of people within 1 standard deviation of the mean?

• 99.7

• 34

• 68

• 95