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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?

Mathematics

ScanSolve AI Answer

Answer

0.5

Step-by-step solution

3 steps

This problem involves a normal distribution.

  1. Identify the given parameters of the normal distribution.

    The average (mean) intelligence of committee members is given as μ=100\mu = 100.
    The standard deviation (SD) is given as σ=14\sigma = 14.
    The distribution is assumed to be a normal distribution.

  2. 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 P(X≤100)P(X \le 100), where XX is the IQ score.

  3. Use the properties of a normal distribution.

    For any normal distribution, the mean (μ\mu) 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.

    P(X≤μ)=0.5P(X \le \mu) = 0.5

    In this case, μ=100\mu = 100.

    P(X≤100)=0.5P(X \le 100) = 0.5

    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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