Distributions and Curves
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Algebra II › Distributions and Curves
Your teacher tells you that the mean score for a test was a 
You are given that the 
Explanation
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 
Your teacher tells you that the mean score for a test was a
You are given that the
Explanation
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
All of the following statements regarding a Normal Distribution are true except:
All of these are true.
A graph of a normally-distributed data set is symmetrical.
A graph of a normally-distributed data set will have a single, central peak at the mean of the data set that it describes.
The shape of the graph of a normally-distributed data set is dependent upon the mean and the standard deviation of the data set that it describes.
Between two graphs of normally-distributed data sets, the graph of the set with a higher standard deviation will be wider than the graph of the set with a lower standard deviation.
Explanation
The graph of a normally-distributed data set is symmetrical.
The graph of a normally-distributed data set has a single, central peak at the mean of the data set that it describes.
The graph of a normally-distributed data set will vary based only upon the mean and the standard deviation of the set that it describes.
The graph of a normally-distributed data set with a higher standard deviation will be wider than the graph of a normally-distributed data set with a lower standard deviation.
The question asks us to find the statement that is not true; however, all statements are true so the correct response is "All of these are true."
All of the following statements regarding a Normal Distribution are true except:
All of these are true.
A graph of a normally-distributed data set is symmetrical.
A graph of a normally-distributed data set will have a single, central peak at the mean of the data set that it describes.
The shape of the graph of a normally-distributed data set is dependent upon the mean and the standard deviation of the data set that it describes.
Between two graphs of normally-distributed data sets, the graph of the set with a higher standard deviation will be wider than the graph of the set with a lower standard deviation.
Explanation
The graph of a normally-distributed data set is symmetrical.
The graph of a normally-distributed data set has a single, central peak at the mean of the data set that it describes.
The graph of a normally-distributed data set will vary based only upon the mean and the standard deviation of the set that it describes.
The graph of a normally-distributed data set with a higher standard deviation will be wider than the graph of a normally-distributed data set with a lower standard deviation.
The question asks us to find the statement that is not true; however, all statements are true so the correct response is "All of these are true."
The scores for your recent english test follow a normal distribution pattern. The mean was a 75 and the standard deviation was 4 points. What percentage of the scores were below a 67?
2.5%
5%
10%
7.5%
Explanation
Use the 68-95-99.7 rule which states that 68% of the data is within 1 standard deviation (in either direction) of the mean, 95% is within 2 standard deviations, and 99.7% is within 3 standard deviations of the mean.
In this case, 95% of the students' scores were between:
75-(2 x 4) and 75+(2 x 4)
or between a 67 and a 83, with equal amounts of the leftover 5% of scores above and below those scores. This would mean that 2.5% of the students scored below a 67% on the test.
The scores for your recent english test follow a normal distribution pattern. The mean was a 75 and the standard deviation was 4 points. What percentage of the scores were below a 67?
2.5%
5%
10%
7.5%
Explanation
Use the 68-95-99.7 rule which states that 68% of the data is within 1 standard deviation (in either direction) of the mean, 95% is within 2 standard deviations, and 99.7% is within 3 standard deviations of the mean.
In this case, 95% of the students' scores were between:
75-(2 x 4) and 75+(2 x 4)
or between a 67 and a 83, with equal amounts of the leftover 5% of scores above and below those scores. This would mean that 2.5% of the students scored below a 67% on the test.
You just took your ACT. The mean score was a 
Explanation
Use the formula for z-score:
Where 
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?
Explanation
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:
On a statistics exam, the mean score was 
Explanation
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 
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?
Explanation
Use the formula for z-score:
Where 
