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41 votes
41 votes
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

Out of a randomly selected 3700 people from the population, how many of them
would have an IQ less than 66, to the nearest whole number?

User Biesior
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1 Answer

8 votes
8 votes
To answer this question, we can use the 68-95-99.7 rule, which states that for a normal distribution, 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

Since we want to find the number of people with an IQ less than 66, which is less than one standard deviation from the mean, we can use the first part of the rule. We know that 68% of the values fall within one standard deviation of the mean, so we can say that 100% * (1 - 0.68) = 32% of the values fall outside of one standard deviation from the mean.

Since the standard deviation of the IQ scores is 15, we can say that 32% of the values fall below the mean - 15 and above the mean + 15. We can also say that 32% of the values fall below 100 - 15 = 85 and above 100 + 15 = 115.

Therefore, out of the 3700 people selected from the population, we can expect that 32% * 3700 = <<32*.01*3700=1184>>1184 of them will have an IQ less than 85 or greater than 115.

Since we are interested in the number of people with an IQ less than 66, we need to subtract the number of people with an IQ greater than 115 from the total. This means that 1184 - (3700 - 1184) = 1184 - 2516 = <<1184-(3700-1184)=1184-2516=-1332>>-1332 of the people selected will have an IQ less than 66.

Since it is not possible for a person to have a negative IQ score, the number of people with an IQ less than 66 is 0.
User Falconcreek
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