Normal Probability Distribution

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.

• 2.5%

• 0.15%

• 2.35%

• 2.25%

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

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%

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

• 99.7

• 34

• 68

• 95

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.