How to find descriptive data from a z-score - AP Statistics
Card 0 of 7
A value has a 
-score of 
. The value is . . .
A value has a
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.
The
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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?
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?
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.
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.
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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?
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
The z-score equation is 
.
To solve for 
we have 
.
The z-score equation is
To solve for
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Your professor gave back the mean and standard deviation of your class's scores on the last exam.
Your friend says the z-score of her exam is 
.
What did she score on her exam?
Your professor gave back the mean and standard deviation of your class's scores on the last exam.
Your friend says the z-score of her exam is
What did she score on her exam?
The z-score is the number of standard deviations above the mean.
We can use the following equation and solve for x.
Two standard deviations above 75 is 85.
The z-score is the number of standard deviations above the mean.
We can use the following equation and solve for x.
Two standard deviations above 75 is 85.
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Your boss gave back the mean and standard deviation of your team's sales over the last month.
Your friend says the z-score of her number of sales is 
.
How many sales did she make?
Your boss gave back the mean and standard deviation of your team's sales over the last month.
Your friend says the z-score of her number of sales is
How many sales did she make?
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.
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.
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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?
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?
To find out your score 
on the test, we enter the given information into the z-score formula and solve for 
.
where 
is the z-score, 
is the mean, and 
is the standard deviation.
As such,
So you scored a 
on the test.
To find out your score
As such,
So you scored a
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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?
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?
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:
where z is the z-score, x is your data point, 
is the mean, 81.15, and 
is the standard deviation, which we are told is 8.41.
multiply both sides by 8.41
we can reasonably round this to 73.5, which is an actual score in the data set. That must be your grade.
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:
where z is the z-score, x is your data point,
multiply both sides by 8.41
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