Normal Distributions & Z-Scores

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

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The z-score represents.....

• the amount of standard deviations a data value is above or below the mean.
• the percentile the data value is above or below the mean.
• the amount of standard deviations a data value is above or below the median.
• the percent the data value is above or below the mean.

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

• 2.5
• -2.5
• 5.2
• -5.2

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If I have a positive z-score, I scored ABOVE or BELOW the mean?

• ABOVE

• BELOW

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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

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Joanne's Z-score is -1.5. What does this mean?

• She didn't take the test yet.

• She scored 1.5 standard deviations below the average.

• She did better than most people.

• No clue

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1) What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 2?

• 25

• 20

• 26

• 68

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1) A group of data with normal distribution has a mean of 45. If one element of the data is 60, will the z-score be positive or negative?

• Positive

• Negative

• Neither

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Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores?

• Jack’s z = 1.07; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 1.07; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.94; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 0.94; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.81; Jill’s z = 0.99; Jill wins the contest

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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

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