Normal Distribution

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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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 22%.

• 69.37 in 
• 67.58 in 
• 73.12 in 

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Given a mean of 75 and a standard deviation of 7, what percentage of scores are greater than 68?

• 34%

• 84%

• 95%

• 68%

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Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 82?

• 475

• 170

• 237

• 80

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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At a high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What GPA do you need to fall in the top 20%? The top 10%?

• 3.40 and 3.67

• 3.67 and 3.40

• 3.80 and 3.90

• 3.20 and 3.10

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The mean life of a tire is 30,000 km. The standard deviation is 2000 km. The company will give you a refund for your tires if they fall in the lowest 5%. How many miles would get you a refund? What is the number of miles that would fall in the top 5%

• 26,700 km and 33,280 km

• 5,000 km and 25,000 km

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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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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 6 days or less?

• 68%
• 34%
• 16%
• 2.5%

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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 ranked top 25 percent. How long was his jump?

• 0.67 inch

• 263 inches

• 272.44 inches

• 277.25 inches