Data Sets And Z-scores

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AP Statistics › Data Sets And Z-scores

Questions 1 - 10

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?

Explanation

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.

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?

Explanation

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

To solve for we have .

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?

Explanation

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.

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

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

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?

Explanation

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.

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?

Explanation

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.

Explanation

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

To solve for we have .

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?

Explanation

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.

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

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

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?

Explanation

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.

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?

Suspect 1

Suspect 2

Suspect 3

Suspect 4

Explanation

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.

Suspect 1: 2.3

Suspect 2: 1.2

Suspect 3: 0.2

Suspect 4: -1.2.

Which of the following suspects committed the crime?

Suspect 1

Suspect 2

Suspect 3

Suspect 4