Question 1

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.

Accepted Answer

To find the probability of a pregnancy lasting more than 300 days, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (300 days), μ is the mean (268 days), and σ is the standard deviation (15 days). Plugging in the values, we get Z = (300 - 268) / 15 = 32 / 15 ≈ 2.13. Looking up 2.13 in the standard normal distribution table gives us the area to the left of Z, which is approximately 0.9834. Since we want the area to the right (the probability of lasting more than 300 days), we subtract this from 1, giving 1 - 0.9834 = 0.0166.

Question 2

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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?

Accepted Answer

The answer of The distribution of cholesterol levels in teenage...

Question 3

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?

Accepted Answer

The probability that a woman's height is between 65.5 and 68.0 inches is the area under the normal distribution curve between those two values. Using a standard normal distribution table, we find that the area between z = (65.5 - 63.6) / 2.5 = 0.76 and z = (68.0 - 63.6) / 2.5 = 1.76 is 0.1844.

Question 4

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

Accepted Answer

To find the probability that a teenage boy has a cholesterol level greater than 200, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (200), $\mu$ is the mean (170), and $\sigma$ is the standard deviation (30). Plugging in the values, we get $Z = \frac{200 - 170}{30} = 1$. Looking up the Z-score of 1 in a standard normal distribution table or using a calculator, we find that the area to the left of Z=1 is approximately 0.8413. Since we want the area to the right (the probability of being greater than 200), we subtract this from 1, resulting in $1 - 0.8413 = 0.1587$.

Question 5

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.

Accepted Answer

We need to find the probability of getting a salary greater than $36,000, which can be calculated using the standard normal distribution formula:

z = (x - μ) / σ

where x is the value we want to find the probability for (i.e. $36,000), μ is the mean salary of elementary school teachers ($32,000) and σ is the standard deviation ($3000).

z = (36,000 - 32,000) / 3000
z = 1.33

Now, we need to find the area under the normal distribution curve to the right of z = 1.33. Using a standard normal distribution table or calculator, we can find this probability to be 0.0918.

Therefore, the best choice is A) 0.0918.

Question 6

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.

Accepted Answer

To find the probability that a teacher makes less than $28,000, we calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value ($28,000), μ is the mean ($32,000), and σ is the standard deviation ($3,000). This gives us Z = ($28,000 - $32,000) / $3,000 = -4,000 / 3,000 = -1.33. Looking up the Z-score of -1.33 in a standard normal distribution table gives us a probability of approximately 0.0918.

Question 7

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose less than 20 suitcases?

Accepted Answer

To find the probability of losing less than 20 suitcases, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is 20, $\mu$ is 15.5, and $\sigma$ is 3.6. Calculating the Z-score gives us $Z = \frac{20 - 15.5}{3.6} = 1.25$. Looking up 1.25 in the Z-table gives us a probability of 0.8944, indicating the probability of losing less than 20 suitcases is 0.8944.

Question 8

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.

Accepted Answer

The answer of The graph depicts IQ scores of adults,...

Question 9

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?

Accepted Answer

Three weeks early is 21 days early. The z-score for this is (21 - 268) / 15 = -1.62. The area to the left of this z-score is 0.0526, or 5.26%. So, the percent of babies born prematurely is 100% - 5.26% = 94.74%.

Question 10

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 U.S. Army requires that the heights of women be between 58 and 80 inches. If a
woman is randomly selected, what is the probability that her height is between 58 and 80 inches?

Accepted Answer

The answer of Assume that the heights of women are...

Question 11

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.

Accepted Answer

To find the IQ score corresponding to a z-score of 1.96, use the formula: IQ = mean + (z-score * standard deviation). Plugging in the values: IQ = 100 + (1.96 * 15) = 129.4.

Question 12

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose between 10 and 20 suitcases?

Accepted Answer

To find the probability of losing between 10 and 20 suitcases, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$. For X = 10, $Z_1 = \frac{10 - 15.5}{3.6} = -1.5278$. For X = 20, $Z_2 = \frac{20 - 15.5}{3.6} = 1.25$. Looking up these Z-scores in a standard normal distribution table or using a calculator, we find the probabilities corresponding to $Z_1$ and $Z_2$, and then subtract the smaller from the larger to find the probability of being between these two values. The calculation gives us approximately 0.8314, indicating the probability of losing between 10 and 20 suitcases in a week.

Question 13

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.

Accepted Answer

The probability of a pregnancy lasting less than 250 days is the area under the normal distribution curve to the left of 250 days. This area is given by the cumulative distribution function (CDF) of the normal distribution, which can be calculated using a calculator or a statistical software package. The CDF of the normal distribution with mean 268 and standard deviation 15 is 0.1151 at 250 days. Therefore, the probability of a pregnancy lasting less than 250 days is 0.1151.

Question 14

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

Accepted Answer

To find the probability that a teenage boy has a cholesterol level greater than 225, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (225), $\mu$ is the mean (170), and $\sigma$ is the standard deviation (30). Plugging in the values, we get $Z = \frac{225 - 170}{30} = \frac{55}{30} = 1.8333$. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability associated with a Z-score greater than 1.8333 is approximately 0.0336.

Question 15

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.

Accepted Answer

To find the percentage of men meeting the height requirements, calculate the z-scores for 64 and 78 inches, then find the area between these z-scores using the standard normal distribution. The z-score for 64 inches is (64-69)/2.8 = -1.79, and for 78 inches is (78-69)/2.8 = 3.21. The area between these z-scores corresponds to approximately 96.26% of the distribution.

Question 16

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose more than 20 suitcases?

Accepted Answer

To find the probability of losing more than 20 suitcases, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X = 20$, $\mu = 15.5$, and $\sigma = 3.6$. This gives $Z = \frac{20 - 15.5}{3.6} = 1.25$. Looking up 1.25 in the Z-table gives the probability of being below 1.25, so we subtract this from 1 to find the probability of being above 1.25, which is approximately 0.1056.

Question 17

Assume that blood pressure readings are normally distributed with $\mu$ = 120 and $\sigma$ = 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?

Accepted Answer

To find the percentage of people with a blood pressure reading greater than 145, we calculate the z-score: $ z = \frac{145 - 120}{8} = 3.125 $. Using the standard normal distribution table, the probability of a z-score greater than 3.125 is approximately 0.09%.

Question 18

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 11. An individualʹs IQ score is found to be 119. Find the z-score corresponding to this value.

Accepted Answer

The z-score is calculated using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values, $z = \frac{(119 - 105)}{11} = \frac{14}{11} = 1.27$.

Question 19

IQ test scores are normally distributed with a mean of 104 and a standard deviation of 15. An individualʹs IQ score is found to be 111. Find the z-score corresponding to this value.

Accepted Answer

The z-score is calculated using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, $z = \frac{(111 - 104)}{15} = \frac{7}{15} = 0.47$.

Question 20

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.

Accepted Answer

The answer of The graph depicts IQ scores of adults,...

Quiz 5: Normal Probability Distributions

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.

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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?

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

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.

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.

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose less than 20 suitcases?

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.

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?

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.

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose between 10 and 20 suitcases?

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.

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

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.

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose more than 20 suitcases?

Assume that blood pressure readings are normally distributed with $\mu$ = 120 and $\sigma$ = 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?

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 11. An individualʹs IQ score is found to be 119. Find the z-score corresponding to this value.

IQ test scores are normally distributed with a mean of 104 and a standard deviation of 15. An individualʹs IQ score is found to be 111. Find the z-score corresponding to this value.

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.

Quiz 5: Normal Probability Distributions

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.

The distribution of cholesterol levels in teenage boys is approximately normal with μ\muμ = 170 and σ\sigmaσ = 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?

The distribution of cholesterol levels in teenage boys is approximately normal with μ\muμ = 170 and σ\sigmaσ = 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.

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.

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.

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\muμ = 15.5 and σ\sigmaσ = 3.6. What is the probability that during a given Week the airline will lose less than 20 suitcases?

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.

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?

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.

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\muμ = 15.5 and σ\sigmaσ = 3.6. What is the probability that during a given Week the airline will lose between 10 and 20 suitcases?

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.

The distribution of cholesterol levels in teenage boys is approximately normal with μ\muμ = 170 and σ\sigmaσ = 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.

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.

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\muμ = 15.5 and σ\sigmaσ = 3.6. What is the probability that during a given Week the airline will lose more than 20 suitcases?

Assume that blood pressure readings are normally distributed with μ\muμ = 120 and σ\sigmaσ = 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?

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 11. An individualʹs IQ score is found to be 119. Find the z-score corresponding to this value.

IQ test scores are normally distributed with a mean of 104 and a standard deviation of 15. An individualʹs IQ score is found to be 111. Find the z-score corresponding to this value.

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.

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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?

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose less than 20 suitcases?

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose between 10 and 20 suitcases?

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 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.

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 $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose more than 20 suitcases?

Assume that blood pressure readings are normally distributed with $\mu$ = 120 and $\sigma$ = 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?