Standard Deviation, Z-scores, and Normal Curve

Calculate the mean from the following data:

12, 18, 24, 32, 34, 39, 45, 52, 63

• $\mu=15.4$

• $\mu=35.4$

• $\mu\ =\ 16.3$

• $\mu\ =\ 34$

Find the standard deviation for the following data:

12, 18, 24, 32, 34, 39, 45, 52, 63

• $\sigma\ =\ 15.4$

• $\sigma=\ 35.4$

• $\sigma\ =\ 16.3$

• $\sigma\ =\ 34$

You have 3 employees that are timed for a certain job related task. You want to promote the most consistent worker. Who would you promote?

A: 12, 18, 24, 30, 36, 42, 48

B: 12, 15, 18, 30, 42, 45, 48

C: 12, 12, 12, 30, 48, 48, 48

• employee A gets promoted

• employee B gets promoted

• employee C gets promoted

For a certain type of computer the length of time between battery charges is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Select the values (2 answers) that represent the range of the charging time within 2 standard deviations of the mean.

• 50

• 35

• 80

• 65

• 20

A class assignment has a mean of 85% and a standard deviation of 6. Find your z-score if you earned a 76% on this assignment.

• z = -1.1

• z = -2.1

• z = - 5

• z = -1.5

A radar unit is used to measure the speed of vehicles on the road. The speeds are normally distributed with a mean of 55 mph and a standard deviation of 10 mph. If the z-score for your speed is -0.8, what is you actual speed?

• 55.8

• 47

• 63

• 43.8

Amy scored a 31 on the math part of the ACT in a year where the mean was 21 with a standard deviation of 5.3.

Stephanie scored a 720 on the math part of the SAT in a year where the mean was 515 and the standard deviation was 116.

Which student scored higher when compared to the other testers.

• Amy

• Stephanie

• They were the same.

The middle of the normal curve is represented by what statistic?

• bell

• mean

• standard deviation

• z-score

What is the area under the normal curve?

• 0.15

• 1

• 13.5

• 34

What percent of the data falls between the z-score of 1 and 2 on the normal curve?

• 34%

• 13.5%

• 2.35%

• .15%

• 100%