Normal Probability

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

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

A standardized test has scores that can be described by a Normal model with a mean score was 100 points and a standard deviation of 10 points. What score is at the 25th percentile?

• 93.26

• 106.74

• 90.32

• 80

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%

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.

This data is normally distributed.  What percent of the data is in 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.

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%

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

• 68%

• 95%

• 99.7%

• 50%

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

• 99.7

• 34

• 68

• 95