Normal Distributions - Algebra II
Card 0 of 4
The ages of the students at GW High School are normally distributed with a mean of 
and a standard deviation of 
years.
What is the proportion of students that are younger than 
years old?
The ages of the students at GW High School are normally distributed with a mean of
What is the proportion of students that are younger than
This question relates to the 
rule of normal distribution. We know that 
of the data are within 
standard deviations from the mean.
In this case this means that 
of the students are between
and 
and 
and 
Therefore we have 
of the students that are outside of this range. Since the normal distribution is symmetric, the proportion of students below 
is the same as the proportion of students above 
.
Thus the right answer is 
or 
.
This question relates to the
In this case this means that
Therefore we have
Thus the right answer is
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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?
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?
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.
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.
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Your class just took a math test. The mean test score was a 78 with a standard deviation of 2 points. With this being the case, 99.7% of the class scored between what two scores?
Your class just took a math test. The mean test score was a 78 with a standard deviation of 2 points. With this being the case, 99.7% of the class scored between what two scores?
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 (in either direction) of the mean.
In this case, 99.7% of the students' scores were between 3 standard deviation above the mean and 3 standard deviations below the mean:
78-(2 x 3) and 78+(2 x 3)
or between a 72 and an 84.
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 (in either direction) of the mean.
In this case, 99.7% of the students' scores were between 3 standard deviation above the mean and 3 standard deviations below the mean:
78-(2 x 3) and 78+(2 x 3)
or between a 72 and an 84.
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All of the following statements regarding a Normal Distribution are true except:
All of the following statements regarding a Normal Distribution are true except:
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 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."
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