5.63 Stealing from a store, continued. Refer to Exercise 5.61.

1. (a) What is the expected number of students in your sample who say that they stole something from a store in the past year? What is the expected number of students who do not say that they stole? You should see that these two means add to 10, the total number of students.

2. (b) What is the standard deviation σ of the number of students in your sample who say that they stole something?

3. (c) Suppose that you live in a city where only 10% of the high school students say that they stole something from a store in the past year. What is σ in this case? What is σ if p = 0.01? What happens to the standard deviation of a binomial distribution as the probability of a success gets close to 0?