Z-scores - Algebra II
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A large group of test scores is normally distributed with mean 78.2 and standard deviation 4.3. What percent of the students scored 85 or better (nearest whole percent)?
A large group of test scores is normally distributed with mean 78.2 and standard deviation 4.3. What percent of the students scored 85 or better (nearest whole percent)?
If the mean of a normally distributed set of scores is 
and the standard deviation is 
, then the 
-score corresponding to a test score of 
is
From a 
-score table, in a normal distribution,
We want the percent of students whose test score is 85 or better, so we want 
. This is
or about 5.7 % The correct choice is 6%.
If the mean of a normally distributed set of scores is
From a
We want the percent of students whose test score is 85 or better, so we want
or about 5.7 % The correct choice is 6%.
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A distributor manufactures a product that has an average weight of 
pounds.
If the standard deviation is 
pounds, determine the z-score of a product that has a weight of 
pounds.
A distributor manufactures a product that has an average weight of
If the standard deviation is
The z-score can be expressed as
where
Therefore the z-score is:
The z-score can be expressed as
where
Therefore the z-score is:
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On a statistics exam, the mean score was 
and there was a standard deviation of 
. If a student's actual score of 
, what is his/her z-score?
On a statistics exam, the mean score was
The z-score is a measure of an actual score's distance from the mean in terms of the standard deviation. The formula is:
Where 
are the mean and standard deviation, respectively. 
is the actual score.
If we plug in the values we have from the original problem we have
which is approximately 
.
The z-score is a measure of an actual score's distance from the mean in terms of the standard deviation. The formula is:
Where
If we plug in the values we have from the original problem we have
which is approximately
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The salaries of employees at XYZ Corporation follow a normal distribution with mean 60,000 and standard deviation 7,500. What proportion of employees earn approximately between 69,000 and 78,000?
Use the normal distribution table to calculate the probabilities. Round your answer to the nearest thousandth.
The salaries of employees at XYZ Corporation follow a normal distribution with mean 60,000 and standard deviation 7,500. What proportion of employees earn approximately between 69,000 and 78,000?
Use the normal distribution table to calculate the probabilities. Round your answer to the nearest thousandth.
Let X represent the salaries of employees at XYZ Corporation.
We want to determine the probability that X is between 69,000 and 78,000:
To approximate this probability, we convert 69,000 and 78,000 to standardized values (z-scores).
We then want to determine the probability that z is between 1.2 and 2.4
The proportion of employees who earn between 69,000 and 78,000 is 0.107.
Let X represent the salaries of employees at XYZ Corporation.
We want to determine the probability that X is between 69,000 and 78,000:
To approximate this probability, we convert 69,000 and 78,000 to standardized values (z-scores).
We then want to determine the probability that z is between 1.2 and 2.4
The proportion of employees who earn between 69,000 and 78,000 is 0.107.
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The mean grade on a science test was 79 and there was a standard deviation of 6. If your sister scored an 88, what is her z-score?
The mean grade on a science test was 79 and there was a standard deviation of 6. If your sister scored an 88, what is her z-score?
Use the formula for z-score:
Where 
is her test score, 
is the mean, and 
is the standard deviation.
Use the formula for z-score:
Where
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You just took your ACT. The mean score was a 
with a standard deviation of 
. If you scored a 
, what is your z-score?
You just took your ACT. The mean score was a 
Use the formula for z-score:
Where 
is your score, 
is the mean, and 
is the standard deviation.
Use the formula for z-score:
Where
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Your teacher tells you that the mean score for a test was a 
and that the standard deviation was 
for your class.
You are given that the 
-score for your test was 
. What did you score on your test?
Your teacher tells you that the mean score for a test was a
You are given that the
The formula for a z-score is
where 
= mean and 
= standard deviation and 
=your test grade.
Plugging in your z-score, mean, and standard deviation that was originally given in the question we get the following.
Now to find the grade you got on the test we will solve for 
.
The formula for a z-score is
where
Plugging in your z-score, mean, and standard deviation that was originally given in the question we get the following.
Now to find the grade you got on the test we will solve for
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In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?
In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?
Write the formula to find the z-score. Z-scores are defined as the number of standard deviations from the given mean.
Substitute the values into the formula and solve for the z-score.
Write the formula to find the z-score. Z-scores are defined as the number of standard deviations from the given mean.
Substitute the values into the formula and solve for the z-score.
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Suppose a student scored a 
on a test. The mean of the tests are 
, and the standard deviation is 
. What is the student's z-score?
Suppose a student scored a
Write the formula for z-score where 
is the data, 
is the population mean, and 
is the population standard deviation.
Substitute the variables.
The z-score is: 
Write the formula for z-score where
Substitute the variables.
The z-score is:
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Suppose Bob's test score is 50. Determine the z-score if the standard deviation is 3, and the mean is 75.
Suppose Bob's test score is 50. Determine the z-score if the standard deviation is 3, and the mean is 75.
Write the formula for z-scores. This tells how many standard deviations above the below the mean.
Substitute the known values into the equation.
The z-score is: 
Write the formula for z-scores. This tells how many standard deviations above the below the mean.
Substitute the known values into the equation.
The z-score is:
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Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2.
Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2.
Write the formula to determine the z-scores.
Substitute all the known values into the formula to determine the z-score.
Simplify this equation.
The answer is: 
Write the formula to determine the z-scores.
Substitute all the known values into the formula to determine the z-score.
Simplify this equation.
The answer is:
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Determine the z-score of a test result is 45, the mean is 60, and the standard deviation is 8.
Determine the z-score of a test result is 45, the mean is 60, and the standard deviation is 8.
Write the formula for z-scores. Z-scores determine the number of standard deviations below or above the mean.
Substitute the values into the formula to determine the z-score.
The z-score is 
.
Write the formula for z-scores. Z-scores determine the number of standard deviations below or above the mean.
Substitute the values into the formula to determine the z-score.
The z-score is
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Suppose Billy scored a 54 on his exam. The mean of the exam grades is 66 and the standard deviation is 3. What is the z-score?
Suppose Billy scored a 54 on his exam. The mean of the exam grades is 66 and the standard deviation is 3. What is the z-score?
Write the formula for z-scores. Z scores determine how many standard deviations a score is above or below the mean.
Substitute the known values in order to determine the z-score.
The answer is: 
Write the formula for z-scores. Z scores determine how many standard deviations a score is above or below the mean.
Substitute the known values in order to determine the z-score.
The answer is:
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Sarah scored an 8.5 out of ten on her gymnastics floor routine. If the mean of the scores is 9.2 and the standard deviation is 1.3, what is her z-score?
Sarah scored an 8.5 out of ten on her gymnastics floor routine. If the mean of the scores is 9.2 and the standard deviation is 1.3, what is her z-score?
Write the formula for z-scores. Z-scores are indicators of how many standard deviations above or below the mean.
Substitute the known values.
The answer is: 
Write the formula for z-scores. Z-scores are indicators of how many standard deviations above or below the mean.
Substitute the known values.
The answer is:
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