Assume you are thinking about starting a Mensa chapter in your hometown, which has a population of about 10,000 people. You need to know how many people would qualify for Mensa, which requires an IQ of at least 130. You realize that IQ is normally distributed with a mean of 100 and a standard deviation of 15 . Complete the following.

1. Find the approximate number of people in your hometown who are eligible for Mensa.

2. Is it reasonable to continue your quest for a Mensa chapter in your hometown?

3. How could you proceed to find out how many of the eligible people would actually join the new chapter? Be specific about your methods of gathering data.

4. What would be the minimum IQ score needed if you wanted to start an Ultra-Mensa club that included only the top \(1 \%\) of IQ scores?