According to the 2010 U. S. Census, 24% of U. S. residents are under 18 years old. Suppose we take a random sample of 500 U. S. residents. Let X = the number of people in the sample who are under 18 years old. 1. Calculate the mean and standard deviation of the sampling distribution of X.
2. Interpret the standard deviation from part (a).
3. Justify that it is appropriate to use a normal distribution to model the sampling distribution of X.
4. Using a normal distribution, calculate the probability that the number of people under 18 years old in a random sample of size 500 is between 100 and 110.