Answer:
15.9%
Explanation:
You want the percentage of people with an IQ less than 85, assuming IQ values are normally distributed with a mean of 100 and a standard deviation of 15.
CDF
The probability of interest can be found using the normalCDF function of a calculator or spreadsheet. The range of X-values, the mean, and the standard deviation are required. Here, we're interested in the probability that X is less than 85, so the interval of interest is (-∞, 85].
The calculator result, rounded to tenths, is shown in the attachment.
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Additional comment
The limit of interest (85) is one standard deviation below the mean:
85 = 100 -15
The "empirical rule" tells us that 68% of a normal distribution is within 1 standard deviation of the mean. That suggests that the percentage in the lower tail is (1 -0.68)/2 = 0.16 = 16%.
The empirical rule is not able to get us to the nearest tenth percent, but it confirms the magnitude of the result we found.