Normal Distribution, Z-Scores & The Empirical Rule

Multiple Choice

What is the average value of a dataset called?

• median

• mean

• mode

• range

Multiple Choice

What is the symbol used to represent the mean in statistics?

• μ

• x

• σ

• n

Multiple Choice

What is the shape of a normal distribution?

• circular

• bell-shaped

• triangular

• rectangular

Multiple Choice

What is the symbol used to represent the standard deviation in statistics?

• μ

• x

• σ

• n

Multiple Choice

For a normal distribution, what proportion of the data is between the mean and one standard deviation above the mean?

• 0.25

• 0.68

• 0.5

• 0.34

Multiple Choice

For a normal distribution, what proportion of the data is above the mean?

• 0.84

• 0.68

• 0.95

• 0.5

Multiple Choice

For a normal distribution, what proportion of the data is above  $$-1\sigma$$  ?

• 0.84

• 0.68

• 0.95

• 0.34

Multiple Choice

According to the 68-95-99.7 rule, what percentage of data falls within one standard deviation of the mean in a normal distribution?

• 50%

• 68%

• 75%

• 90%

Multiple Choice

In a normal distribution, what percentage of data falls within two standard deviations of the mean according to the 68-95-99.7 rule?

• 50%

• 95%

• 99.7%

• 68%

Multiple Choice

In a normal distribution, what percentage of data falls within three standard deviations of the mean according to the 68-95-99.7 rule?

• 68%

• 95%

• 50%

• 99.7%

Multiple Choice

This graph shows a shaded area under the curve of a standard normal distribution. This shows the percentage of data that falls......

• below the data value associated with a z-score of 1.

• above the data value associated with a z-score of 1.

Multiple Choice

The graph shows the percentage of data that falls...

• above a z-score of -1

• below a z-score of -1

Multiple Choice

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?

• 2.5%

• .15%

• 2.35%

• 2.25%

Multiple Choice

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.4. What proportion of weeks would you expect to have less than 5 accidents?

• 0.5

• 0.16

• 0.025

• 0.34

Multiple Choice

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the proportion of golfers that are older than 42.

• 13.5%

• 16%

• 50%

• 85%

Multiple Choice

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

There are 500 golf members at the Mathy Country Club. How many are younger than 34?

• 16

• 80

• 100

• 150