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6 votes
6 votes
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of scores will fall between 70 and 115?

User Ian Selby
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1 Answer

17 votes
17 votes

We are given a normal distribution with a mean of 100 and a standard deviation of 15. We are asked for the percentage of values between 70 and 115. To do that, we need to have into account that in the normal distribution with a mean of 100 and a standard deviation of 15 the value 115 is one standard deviation from the mean, which means that 34.1% of the values will fall between 100 and 115. The value of 70 is 2 standard deviations to the left of the mean, this means that 47.7% of the values will fall between 70 and 100. The total percentage of values between 70 and 115 is:


47.7+34.1=81.8

therefore the percentage is 81.1%

User Jared Brown
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