This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
This problem involves a normal distribution. Step 1: Identify the given parameters of the normal distribution. The average (mean) intelligence of committee members is given as = 100. The standard deviation (SD) is given as = 14. The distribution is assumed to be a normal distribution. Step 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), where X is the IQ score. Step 3: 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. P(X ) = 0.5 In this case, = 100. P(X 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. Last free one today — make it count tomorrow, or type /upgrade for unlimited.