5.61 Stealing from a store. A survey of more than 20,000 U.S. high school students revealed that 20% of the students say that they stole something from a store in the past year.17 This is down 7% from the last survey, which was performed two years earlier. You decide to take a random sample of 10 high school students from your city and ask them this question.
(a) If the high school students in your city match this 20% rate, what is the distribution of the number of students who say that they stole something from a store in the past year? What is the distribution of the number of students who do not say that they stole something from a store in the past year?
(b) What is the probability that four or more of the 10 students in your sample say that they stole something from a store in the past year?