Finding Probabilities with Normal Distribution

Assume that the random variable X is normally distributed, with mean μ = 80 and standard deviation σ = 15.

Compute the probability P(X > 92).

• 0.1977

• 0.2119

• 0.7881

• 0.2420

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IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹ s IQ

score is found to be 110. Find the z- score corresponding to this value.

• -0.67

• 1.33

• 0.67

• -1.33

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The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard

deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days.

• 0.0166

• 0.9834

• 0.2375

• 0.3189

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The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source:

U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a

teenage boy has a cholesterol level greater than 200.

• 0.3419

• 0.1587

• 0.8314

• 0.2138

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An airline knows from experience that the distribution of the number of suitcases that get lost each week on a

certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given

week the airline will lose less than 20 suitcases?

• 0.3944

• 0.1056

• 0.4040

• 0.8944

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Assume that the salaries of elementary school teachers in the United States are normally distributed with a

mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that

he or she makes more than $36,000.

• 0.9802

• 0.2113

• 0.0918

• 0.9827

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The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard

deviation of 15 days. A baby is premature if it is born three weeks early. What percent of babies are born

prematurely?

• 6.81 %

• 9.21 %

• 8.08 %

• 10.31 %

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The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source:

U.S. National Center for Health Statistics). Levels above 200 warrant attention. What percent of teenage boys

have levels between 170 and 225?

• 46.64 %

• 3.36 %

• 6.06 %

• 56.13 %

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Assume that blood pressure readings are normally distributed with μ = 120 and σ = 8. A blood pressure

reading of 145 or more may require medical attention. What percent of people have a blood pressure reading

greater than 145?

• 0.09 %

• 99.91 %

• 6.06 %

• 11.09 %

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Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard

deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find

the percent of men meeting these height requirements.

• 31.12 %

• 99.93 %

• 3.67 %

• 96.26 %

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