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Answer :
a. About 68% of people have an IQ between 85 and 115.
b. Approximately 16% of people have an IQ greater than 115.
c. Almost 2.5% of people have an IQ less than 130.
d. Approximately 0.1% of people have an IQ less than 70.
The Empirical Rule, which is also known as the 68-95-99.7 Rule, is a statistical rule that is often used to estimate the percentage of data values that will be within a certain range of the mean in a normal distribution. This rule states that about 68% of data values will be within one standard deviation of the mean, 95% of data values will be within two standard deviations of the mean, and 99.7% of data values will be within three standard deviations of the mean.Using this rule, we can estimate the percentages of people that fall within certain IQ ranges for this standardized test of intelligence.
For part (a), we want to find the percentage of people that have an IQ between 85 and 115. Since the mean IQ is 100 and the standard deviation is 15, an IQ of 85 is one standard deviation below the mean and an IQ of 115 is one standard deviation above the mean. Therefore, we can use the Empirical Rule to estimate that about 68% of people have an IQ between 85 and 115.
For part (b), we want to find the percentage of people that have an IQ greater than 115. Since an IQ of 115 is one standard deviation above the mean, we can use the Empirical Rule to estimate that about 16% of people have an IQ greater than 115.
For part (c), we want to find the percentage of people that have an IQ less than 130. Since an IQ of 130 is two standard deviations above the mean, we can use the Empirical Rule to estimate that almost 2.5% of people have an IQ less than 130.
For part (d), we want to find the percentage of people that have an IQ less than 70. Since an IQ of 70 is two standard deviations below the mean, we can use the Empirical Rule to estimate that approximately 0.1% of people have an IQ less than 70.
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