Review Question 7, 9.EOC.2 HW Score: $32.73 \%, 5.56$ of 17 points Points: 0 of 1 Save IQ scores based on the Stanford-Binet IQ test are normally distributed with a mean of 100 and standard deviation 15 . If you were to obtain 100 different simple random samples of size 20 from the population of all aduit humans and determine $95 \%$ confidence intervals for each of them, how many of the intervals would you expect to include 100 ? One would expect $\square$ of the 100 intervals to include the mean 100. (Round to the nearest integer as needed.)

Step 1 ：IQ scores based on the Stanford-Binet IQ test are normally distributed with a mean of 100 and standard deviation 15. If you were to obtain 100 different simple random samples of size 20 from the population of all adult humans and determine 95% confidence intervals for each of them, the question asks how many of the intervals would you expect to include 100.

Step 2 ：We can calculate the expected number of intervals that include the mean by multiplying the total number of intervals by the percentage of confidence.

Step 3 ：Let's denote the total number of intervals as \(I\) and the percentage of confidence as \(P\). The expected number of intervals that include the mean can be calculated as \(E = I \times P\).

Step 4 ：Substituting the given values, \(I = 100\) and \(P = 0.95\), into the formula, we get \(E = 100 \times 0.95 = 95\).

Step 5 ：Final Answer: One would expect \(\boxed{95}\) of the 100 intervals to include the mean 100.