Normal Distribution, Z scores, Precentiles

List each set of data by color from the lowest standard deviation to the highest standard deviation.

• blue, green, pink, red

• red, pink, green, blue

• pink, green, red, blue

• blue, green, red, pink

Look at each data set's standard deviation.

Set 1: 15.9

Set 2: 14.64

Set 3: 17.88

Which set of data has values that are closer in relation to the mean value of the data?

• Set 1

• Set 2

• Set 3

• Not enough information is provided

1. Which of the following illustrations represents normal distribution?

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The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  

• 2
• 1
• -2
• -1

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

• 2.5
• -2.5
• 5.2
• -5.2

Brian scored an 80% on a Chemistry Exam. The average on the exam was a 68%, with a standard deviation of 5%. What is Brian's z-score?

• 2.4

• -2.4

• 1.1

• -1.1

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

• 115
• 130.75
• 145
• 120

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees.  What is the z-score for a temperature of 17 degrees?  

• 1 
• 1.43
• -1.43
• 11.5

A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?

• 115

• 120

• 119

• 118

If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?

• -1.25
• +1.25
• +1.20
• +1.02