Unit 6.2 the z score

Multiple Choice

Use the image of the normal graph provided. What is the value of the mean?

• 6

• 34

• 52

• 70

Multiple Choice

Use the image of the normal graph provided. What is the value of the standard deviation?

• 6

• 12

• 36

• 18

Multiple Choice

Which of the following statements best describes what a z-score represents in a normal distribution?

• The probability of an event occurring

• The number of standard deviations a value is from the mean

• The average of all data values

• The total area under the curve

Multiple Choice

Which table is used to find percentiles for the standard normal distribution?

• Standard Normal Table

• T-Distribution Table

• Chi-Square Table

• F-Distribution Table

Multiple Choice

If the area to the left of z is 0.0188, what is the z-score?

• -2.1

• -2.08

• -2.07

• -2.0

Multiple Choice

If the area to the left of z is 96.70%, what is the z-score?

• 1.84

• 1.74

• 1.9

• 1.6

Open Ended

Explain why the z-score should be negative when the area to the right of z is greater than 50%.

Multiple Choice

Find z if the normal curve area to the right of z is 89.61%.

• z = -1.26

• z = 1.26

• z = -0.89

• z = 0.89

Multiple Select

Find z if the normal curve area between 0 and z is 0.4066.

• z = 1.32

• z = 0.91

• z = -1.32

• z = -0.91

Multiple Select

Find z if the normal curve area between 0 and z is 0.2123.

• z = 0.56

• z = 0.21

• z = -0.56

• z = -.021

Open Ended

Explain how you would find the z-score if the area to the left is 0.0116. What steps would you take?

Open Ended

Explain how you would find the area to the right of z = 0.0116

Open Ended

Explain how you would find the area between 0 and z = 0.0116

Multiple Select

Which of the following are objectives for learning about z-scores in normal distributions?

• Find z-scores given the area under the normal curve

• Transform data values (x-values) to z-scores

• Transform z-scores to data values (x-values)

• Calculate the median of a data set

Draw

Given μ = 146, σ = 14, and x = 178, calculate the z-score. Show your work.

Draw

The formula to convert an x-value to a z-score is z = ___

Multiple Choice

What is the formula for calculating the z-score, and what do each of the variables represent?

• z = (x - μ) / σ; z is the z-score, x is the data value, μ is the mean, σ is the standard deviation

• z = (μ - x) / σ; z is the z-score, x is the mean, μ is the data value, σ is the standard deviation

• z = (x - σ) / μ; z is the z-score, x is the data value, μ is the standard deviation, σ is the mean

• z = (x + μ) / σ; z is the z-score, x is the data value, μ is the mean, σ is the standard deviation

Draw

Use your calculator and show all steps

Open Ended

Convert x = 12 into a z-score using μ = 9.5 and σ = 2.3.