5.2 Normal Distribution Finding Probabilities

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 90. Find the z-score corresponding to this value.

-0.67

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

The distribution of cholesterol levels in teenage boys is approximately normal with u=170 and o=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 225.

0.0336

Assume that blood pressure readings are normally distributed with u=120 and o=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%

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 less than $28,000.

0.0918

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.

0.0918

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 more than 20 suitcases?

0.1056

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 less than 250 days.

0.1151

The distribution of cholesterol levels in teenage boys is approximately normal with u=170 and 0=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.

0.1587

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The cheerleaders for a local professional basketball team must be between 65.5 and 68.0 inches. If a woman is randomly selected, what is the probability that her height is between 65.5 and 68.0 inches?

0.1844

Assume that the random variable X is normally distributed, with mean u=100 and standard deviation o=15 Compute the probability P(X > 112).

0.2119

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 17. An individual's IQ score is found to be 112. Find the z-score corresponding to this value.

0.41

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 110. Find the z-score corresponding to this value.

0.67

The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a member selected at random is from the shaded area of the graph.

0.7486

The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a member selected at random is from the shaded area of the graph.

0.7938

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 between 10 and 20 suitcases?

0.8314

Assume that the random variable X is normally distributed, with mean u=90 and standard deviation 0=12 Compute the probability P(57 < X < 105).

0.8914

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?

0.8944

Assume that the random variable X is normally distributed, with mean u=70 and standard deviation o=16 Compute the probability P(X < 90).

0.8944

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 120. Find the z-score corresponding to this value.

1.33

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 13. An individual's IQ score is found to be 126. Find the z-score corresponding to this value.

1.62

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a z-score of 1.96.

129.4

The distribution of cholesterol levels in teenage boys is approximately normal with u=170 and o=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?

3.36%

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?

8.08%

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.

96.26%