Normal Distribution and Probability

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%

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%

• 34%

• 16%

• 2.5%

Find the area under the standard normal curve between z = -2.55 and z = 1.08.

• 0.8545

• 0.7560

• 0.3110

• 0.2140

What is the probability of choosing a Honda? 

• .5970

• .5373

• .4627

• .4030

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 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.

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