How to find descriptive data from a z-score - AP Statistics

Card 0 of 28

Question

A value has a -score of . The value is . . .

Answer

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive -score is always above the mean and a negative -score is always below it. Here, we know the value is below the mean because we have a negative -score.

Compare your answer with the correct one above

Question

There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:

Suspect 1: 2.3

Suspect 2: 1.2

Suspect 3: 0.2

Suspect 4: -1.2.

Which of the following suspects committed the crime?

Answer

Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit.

Compare your answer with the correct one above

Question

All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of and a standard deviation of . Sally's z-score is . What is her score on the test?

Answer

The z-score equation is $z= (x-\mu)/\sigma$ .

To solve for we have .

Compare your answer with the correct one above

Question

Your professor gave back the mean and standard deviation of your class's scores on the last exam.

$\mu=75$

$\sigma=5$

Your friend says the z-score of her exam is .

What did she score on her exam?

Answer

The z-score is the number of standard deviations above the mean.

We can use the following equation and solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-75}{5}=2$

Two standard deviations above 75 is 85.

Compare your answer with the correct one above

Question

Your boss gave back the mean and standard deviation of your team's sales over the last month.

$\mu=35$

$\sigma=3$

Your friend says the z-score of her number of sales is .

How many sales did she make?

Answer

The z-score is the number of standard deviations above or below the mean.

We can use the known information with the following formula to solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-35}{3}=-1$

Compare your answer with the correct one above

Question

Your teacher gives you the z-score of your recent test, and says that the mean score was a 60, with a standard deviation of 6. Your z-score was a -2.5. What did you score on the test?

Answer

To find out your score on the test, we enter the given information into the z-score formula and solve for .

$z=\frac{x-\mu }{\sigma }$ where is the z-score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

As such,

$-2.5=\frac{x- 60}{6 }$

So you scored a on the test.

Compare your answer with the correct one above

Question

The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. If you scored 0.91 standard deviations worse than the mean, what was your score?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Answer

To work with a z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.

We know that your score is 0.91 standard deviations WORSE than the mean, which means that your z-score is -0.91. We can use the following formula for the z-score:

$\small z = \frac{x - \mu }{\sigma }$

where z is the z-score, x is your data point, $\small \mu$ is the mean, 81.15, and $\sigma$ is the standard deviation, which we are told is 8.41.

$\small -0.91 = \frac{x - 81.15 }{8.41 }$

multiply both sides by 8.41

$\small -7.6531 = x - 81.15$

$\small 73.4969 = x$ we can reasonably round this to 73.5, which is an actual score in the data set. That must be your grade.

Compare your answer with the correct one above

Question

There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:

Suspect 1: 2.3

Suspect 2: 1.2

Suspect 3: 0.2

Suspect 4: -1.2.

Which of the following suspects committed the crime?

Answer

Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit.

Compare your answer with the correct one above

Question

A value has a -score of . The value is . . .

Answer

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive -score is always above the mean and a negative -score is always below it. Here, we know the value is below the mean because we have a negative -score.

Compare your answer with the correct one above

Question

All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of and a standard deviation of . Sally's z-score is . What is her score on the test?

Answer

The z-score equation is $z= (x-\mu)/\sigma$ .

To solve for we have .

Compare your answer with the correct one above

Question

Your professor gave back the mean and standard deviation of your class's scores on the last exam.

$\mu=75$

$\sigma=5$

Your friend says the z-score of her exam is .

What did she score on her exam?

Answer

The z-score is the number of standard deviations above the mean.

We can use the following equation and solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-75}{5}=2$

Two standard deviations above 75 is 85.

Compare your answer with the correct one above

Question

Your boss gave back the mean and standard deviation of your team's sales over the last month.

$\mu=35$

$\sigma=3$

Your friend says the z-score of her number of sales is .

How many sales did she make?

Answer

The z-score is the number of standard deviations above or below the mean.

We can use the known information with the following formula to solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-35}{3}=-1$

Compare your answer with the correct one above

Question

Your teacher gives you the z-score of your recent test, and says that the mean score was a 60, with a standard deviation of 6. Your z-score was a -2.5. What did you score on the test?

Answer

To find out your score on the test, we enter the given information into the z-score formula and solve for .

$z=\frac{x-\mu }{\sigma }$ where is the z-score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

As such,

$-2.5=\frac{x- 60}{6 }$

So you scored a on the test.

Compare your answer with the correct one above

Question

The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. If you scored 0.91 standard deviations worse than the mean, what was your score?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Answer

To work with a z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.

We know that your score is 0.91 standard deviations WORSE than the mean, which means that your z-score is -0.91. We can use the following formula for the z-score:

$\small z = \frac{x - \mu }{\sigma }$

where z is the z-score, x is your data point, $\small \mu$ is the mean, 81.15, and $\sigma$ is the standard deviation, which we are told is 8.41.

$\small -0.91 = \frac{x - 81.15 }{8.41 }$

multiply both sides by 8.41

$\small -7.6531 = x - 81.15$

$\small 73.4969 = x$ we can reasonably round this to 73.5, which is an actual score in the data set. That must be your grade.

Compare your answer with the correct one above

Question

There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:

Suspect 1: 2.3

Suspect 2: 1.2

Suspect 3: 0.2

Suspect 4: -1.2.

Which of the following suspects committed the crime?

Answer

Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit.

Compare your answer with the correct one above

Question

A value has a -score of . The value is . . .

Answer

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive -score is always above the mean and a negative -score is always below it. Here, we know the value is below the mean because we have a negative -score.

Compare your answer with the correct one above

Question

All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of and a standard deviation of . Sally's z-score is . What is her score on the test?

Answer

The z-score equation is $z= (x-\mu)/\sigma$ .

To solve for we have .

Compare your answer with the correct one above

Question

Your professor gave back the mean and standard deviation of your class's scores on the last exam.

$\mu=75$

$\sigma=5$

Your friend says the z-score of her exam is .

What did she score on her exam?

Answer

The z-score is the number of standard deviations above the mean.

We can use the following equation and solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-75}{5}=2$

Two standard deviations above 75 is 85.

Compare your answer with the correct one above

Question

Your boss gave back the mean and standard deviation of your team's sales over the last month.

$\mu=35$

$\sigma=3$

Your friend says the z-score of her number of sales is .

How many sales did she make?

Answer

The z-score is the number of standard deviations above or below the mean.

We can use the known information with the following formula to solve for x.

$\frac{x-\mu}{\sigma}=z$

$\frac{x-35}{3}=-1$

Compare your answer with the correct one above

Question

Your teacher gives you the z-score of your recent test, and says that the mean score was a 60, with a standard deviation of 6. Your z-score was a -2.5. What did you score on the test?

Answer

To find out your score on the test, we enter the given information into the z-score formula and solve for .

$z=\frac{x-\mu }{\sigma }$ where is the z-score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

As such,

$-2.5=\frac{x- 60}{6 }$

So you scored a on the test.

Compare your answer with the correct one above

Tap the card to reveal the answer