Normal Distribution Practice

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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CCSS.HSS.ID.A.4

The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 3 pounds. A beagle is randomly selected. Find the probability that the beagle’s weight is more than 29 pounds.

• 0.3694
• 0.3781
• 0.0912

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CCSS.HSS.ID.A.4

The weights of miniature horses are roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds.

What is the probability that a miniature horse randomly selected weighs less than 140 pounds?

• .4772

• .0228

• .9544

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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 more than 7 accidents?

• 0.3446
• 0.2856
• 0.4
• 0.6554

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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

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

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CCSS.HSS.ID.A.4

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

• 0.67 inch
• 263 inches
• 272.44 inches
• 277.25 inches

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.3

The weights of paper discarded each week by households are normally distributed with a mean of 9.43 pounds and a standard deviation of 4.17 pounds. What percent of households discard between 10 and 12 pounds?

• 17.68%

• 6.50%

• 28.55%

• 82.32%

The weights of paper discarded each week by households are normally distributed with a mean of 9.43 pounds and a standard deviation of 4.17 pounds. What percent of households throw out fewer than 2 pounds of paper each week?

• 96.26%

• 48.13%

• 3.74%

• 1.87%

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CCSS.HSS.ID.A.4

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 17.5% .

• 69.98 in

• 71.18 in

• 72.40 in

• 73.01 in

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CCSS.HSS.ID.A.4