Review for Quiz - Normal Distributions, Empirical Rule, Z-Scores

A z-score tells you...

• the standard deviation of a sampling distribution.
• the original raw score on which it is based.
• if the distribution it comes from is normal.
• how many standard deviations away from the mean a score lies.

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

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CCSS.HSS.ID.A.4

Calculate the z score of your value if the mean is 75, your score is 90 and the standard deviation is 4.5

• -3.33
• 3.33

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.
• 24,000 km and 34,000 km.
• 26,000 km and 34,000 km.
• 27,000 km and 31,000 km.

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CCSS.HSS.ID.A.4

If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall? 

• -5
• -2
• 2
• 5

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CCSS.HSS.ID.A.4

In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. If 10 000 cookies were produced, how many cookies are within 2 g of the mean?

• 6800

• 9500

• 3200

• 9750

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CCSS.HSS.ID.A.4

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

• 68%

• 99.7%

• 95%

• 34%

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CCSS.HSS.ID.A.4

The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. What percentage of cars averaged less than 85 km/h?

• .15%

• 2.35%

• 2.5%

• 18.5%

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CCSS.HSS.ID.A.4

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%
• 99.7%
• 95%
• 84%

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CCSS.HSS.ID.A.4

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915
• 0.1762
• 0.8238
• -0.93

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CCSS.HSS.ID.A.4