Applications of the Normal Distribution

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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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 is the probability that in a week there would be fewer (less) than 5 accidents?

• 0.6915

• 0.1762

• 0.8238

• -0.93

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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 is the probability that in a week there would be more than 7 accidents?

• 0.3446

• 0.2856

• 0.4

• 0.6554

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CCSS.HSS.ID.A.4

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.

If waist sizes are normally distributed, estimate the probability that a teenager will have a waist size greater than 31 inches.

• .924

• .105

• .16

• .076

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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.

What is the approximate probability that a product will last between 12 and 15 days?

• .68

• .34

• .16

• .025

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CCSS.HSS.ID.A.4

Which is NOT true about the standard normal distribution?

• It is bell-shaped.

• It is not skewed left or right.

• The total area under the curve is 1.

• It is asymmetrical.

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CCSS.HSS.ID.A.4

The mean July daily rainfall in Hulu Kinta is 10 mm and the standard deviation is 1.5 mm

Assume that this data is normally distributed.

How many days in July would you expect the daily rainfall to be less than 8.5 mm? (Find the z-score, and look it up. Then, multiply by 31 days!)

• 5

• 6

• 7

• 10

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CCSS.HSS.ID.A.4

If the value we are looking for is smaller than the mean, the value of z is:

• Not enough information

• Negative

• Positive

• 0

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CCSS.HSS.ID.A.4

If the value we are looking for is the same as the mean, the value of z is:

• Not enough information

• Positive

• Negative

• 0

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CCSS.HSS.ID.A.4

What's the probability x < 13?

(Mean = 10, Variance = 4)

• 0.9332

• 0.2266

• 0.7734

• 0.0668

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CCSS.HSS.ID.A.4