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Assuming IQ scores are normally distributed with a mean of 100 and a standard deviation of 14, what proportion of individuals would have an IQ of 100 or less?
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Step-by-step solution
3 stepsThis problem involves a normal distribution.
Identify the given parameters of the normal distribution.
The average (mean) intelligence of committee members is given as .
The standard deviation (SD) is given as .
The distribution is assumed to be a normal distribution.Determine the probability to be calculated.
We need to find the proportion of women who would have an IQ of 100 or less. This can be written as , where is the IQ score.
Use the properties of a normal distribution.
For any normal distribution, the mean () is also the median. This means that exactly 50% of the data falls below the mean, and 50% of the data falls above the mean.
Therefore, the probability of a randomly selected value being less than or equal to the mean is 0.5.In this case, .
The proportion of women expected to have an IQ of 100 or less is 0.5, or 50%.
The final answer is 0.5.
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