SOLUTION: Hello, I would appreciate it very much to get assistance with a problem: Scores of an IQ Test have a bell-shaped distribution with a mean of 100 and a standard deviation of 1

Question 1141703: Hello,
I would appreciate it very much to get assistance with a problem:
Scores of an IQ Test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the Empirical Rule to determine:
a.What percentage of people have an IQ score between 66 and 134?
b.What percentage of people have an IQ score less than 66 or greater than 134?
c.What percentage of people have an IQ score greater than 151?
Thank you in advance!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 100.
standard deviation is 17

here's a reference on the empirical rule.

https://www.algebra.com/tutors/faq.mpl

if the mean is 100 and the standard deviation is 17, you get the following.

plus or minus 1 standard deviation gets you scores between 83 and 117.

plus or minus 2 standard deviations gets you scores between 66 and 134.

plus or minus 3 standard deviations gets you scores between 49 and 151.

answers to your questions are shown below.

a.What percentage of people have an IQ score between 66 and 134?

95% because this is 2 standard deviations above and below the mean.

b.What percentage of people have an IQ score less than 66 or greater than 134?

5% because 100% - 95% = 5%.

c.What percentage of people have an IQ score greater than 151?

99.7% have scores between 49 and 151.

that leaves 100% - 99.7% = .3% outside those boundaries.

half of those will be below the threshold of 49 and half of those will be above the threshold of 151.

that means .15% will have IQ scores greater than 151.

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