Data Sets And Z-scores - AP Statistics
Card 0 of 72
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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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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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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What is the 
-score for a value of 115 when the mean of the population is 103 and the standard deviation is 8?
What is the
A 
-score indicates whether a particular value is typical for a population or data set. The closer the 
-score is to 0, the closer the value is to the mean of the population and the more typical it is. The 
-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.
A
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A population of values has a mean of 43 and a standard deviation of 12. One of the values in the population is 49. What is the Z-score for that value?
A population of values has a mean of 43 and a standard deviation of 12. One of the values in the population is 49. What is the Z-score for that value?
A Z-score indicates whether a particular value is typical for a population or data set. The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is. The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.
A Z-score indicates whether a particular value is typical for a population or data set. The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is. The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.
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This past week, the temperature has fluctuated quite a bit. From Monday to Sunday, temperatures in Fahrenheit have been the following: 62, 68, 52, 40, 78, 72, 60. The standard deviation is given as 13 and does not need to be calculated. Convert these daily temperatures into z-scores and give the days that are at least one standard deviation away from the mean.
This past week, the temperature has fluctuated quite a bit. From Monday to Sunday, temperatures in Fahrenheit have been the following: 62, 68, 52, 40, 78, 72, 60. The standard deviation is given as 13 and does not need to be calculated. Convert these daily temperatures into z-scores and give the days that are at least one standard deviation away from the mean.
To convert the temperatures into the z-scores, subtract the mean temperature (61.7) from the daily temperatures and divide this by the given standard deviation (13). The daily z-scores are .02, .53, -.81, -1.8, 1.4, .86, and -.14. Recall that z-scores tell you how many standard deviations away from the mean a given observation is.
Only Thursday and Friday are greater than one.
To convert the temperatures into the z-scores, subtract the mean temperature (61.7) from the daily temperatures and divide this by the given standard deviation (13). The daily z-scores are .02, .53, -.81, -1.8, 1.4, .86, and -.14. Recall that z-scores tell you how many standard deviations away from the mean a given observation is.
Only Thursday and Friday are greater than one.
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This year's harvest, the apples had a mean mass of 
with a standard deviation of 
. You pick an apple from the harvest and find its mass to be 
.
What is the z-score of the apple you picked?
This year's harvest, the apples had a mean mass of
What is the z-score of the apple you picked?
To find the z-score, we follow the formula
where 
is the given value, 
is the mean, and 
is the standard deviation.
For this problem we see that
and
Substituting for these values we see
To find the z-score, we follow the formula
For this problem we see that
Substituting for these values we see
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The average score on the statistics final exam was 85 and the standard deviation was 
. Chris scored a 
. Chris scored higher than what percent of his class?
The average score on the statistics final exam was 85 and the standard deviation was
The first step in this problem is calculating the z-score. 
The next step is to look up 4 in the z-table. The value from the table is 
.
The first step in this problem is calculating the z-score.
The next step is to look up 4 in the z-table. The value from the table is
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A population has a standard deviation of 
and a mean of 
. One of the values in the population is 
. What is the z score for that value?
A population has a standard deviation of
A z score is unique to each value within a population.
To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.
A z score is unique to each value within a population.
To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.
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Natalie took her university placement examinations in Spanish and math. In Spanish, she scored 82; in math, she scored 86. The results of the Spanish exam had a mean of 72 and a standard deviation of 8. The results of the math exam had a mean of 68 and a standard deviation of 12. On which exam did Natalie do better, compared with the rest of her peers taking these placement exams?
Natalie took her university placement examinations in Spanish and math. In Spanish, she scored 82; in math, she scored 86. The results of the Spanish exam had a mean of 72 and a standard deviation of 8. The results of the math exam had a mean of 68 and a standard deviation of 12. On which exam did Natalie do better, compared with the rest of her peers taking these placement exams?
We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:
Her z-score for the Spanish exam is 
, which equals 1.25, while her z-score for the math exam is 
, which equals 1.50. Since both z-scores are positive, Natalie did above average on both tests, but since her z-score for the math exam is higher than her z-score for the Spanish exam, Natalie did better on her math exam when compared to the rest of her peers taking the exam.
We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:
Her z-score for the Spanish exam is
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The z-score is also known as the standard score.
The average temperature for all the days preceding the last for the month of February was 55 degrees Farhenheit, with a standard deviation of 5 degrees.
On the last day, the temperature was 73 degrees F. What is the z-score for the temperature on the last day?
The z-score is also known as the standard score.
The average temperature for all the days preceding the last for the month of February was 55 degrees Farhenheit, with a standard deviation of 5 degrees.
On the last day, the temperature was 73 degrees F. What is the z-score for the temperature on the last day?
To find the z-score, follow the formula
or
To find the z-score, follow the formula
or
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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. How many standard deviations are you away from the mean if you scored an 86? \[find your z-score\]
The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. How many standard deviations are you away from the mean if you scored an 86? \[find your z-score\]
To calculate the z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
To calculate your z-score and discover how close your score is to the mean in terms of standard deviations, use this formula:
where x is your data point, 86, 
is the mean, 81.15, and 
is the standard deviation, which we are told is 8.41.
To calculate the z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
To calculate your z-score and discover how close your score is to the mean in terms of standard deviations, use this formula:
where x is your data point, 86,
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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. How many standard deviations are you away from the mean if you got all the questions right? \[find your z-score\]
The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. How many standard deviations are you away from the mean if you got all the questions right? \[find your z-score\]
To calculate the z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
To calculate your z-score and discover how close your score is to the mean in terms of standard deviations, use this formula:
where x is your data point, 100, 
is the mean, 81.15, and 
is the standard deviation, which we are told is 8.41.
To calculate the z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
To calculate your z-score and discover how close your score is to the mean in terms of standard deviations, use this formula:
where x is your data point, 100,
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The observed times (in minutes) it takes a swimmer to complete a race are normally distributed. The z-score for her swimming time this week is 
. Which one of the following statements is correct interpretation of this z-score?
The observed times (in minutes) it takes a swimmer to complete a race are normally distributed. The z-score for her swimming time this week is
The z-score = 
and a negative z-score indicates that the x-value is below the average. The value of the score represents the difference between the x-value and the mean in terms of the number of standard deviations.
The z-score =
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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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