Probability Distributions

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

• -1.33

• 1.33

• 0.88

• 1.02

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 more than 7 accidents?

• 0.3446

• 0.2856

• 0.4

• 0.6554

What is the the total area under the standard normal distribution curve?

• 100

• 25

• .5

• 1

μ = 70 , σ = 8 , X = 50 . Find z score

• 2.5

• -2.5

• 5.2

• -5.2

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%

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. 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.

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%