1. A basketball player makes 40% of her free throws. She takes 5 free throws in a game. If the shots are independent of each other, the probability that she makes 3 out of the 5 shots is about.
A. 0.115
B. 0.230
C. 0.023
2. A small class has 10 students. Seven of the students are male and 3 are female. You write the name of each student on a small card. The cards are shuffled thoroughly and you choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled and you again choose a card at random, observe the name, and replace it in the set. This is done a total of five times. Let X be the number of cards observed in these 5 trials with a name corresponding to a male student. The random variable X has which of the following probability distribution?
A. the binomial distribution, with parameters n = 5 and p = 0.3
B. the binomial distribution, with parameters n = 5 and p = 0.7
C. the normal distribution, with mean 3 and variance 1
D. none of the above
3. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing machine make calls. X is the number of calls until the first live person answers. Does X have a binomial distribution? Give your reasons.
A. No, the calls are not independent.
B. No, the calls are ndependent, but teach one has more than two possibilities
C. No, the calls are independent but there is no fixed number of observations
D. Yes, the calls are independent, each one has two possibilities and the probability of reaching a live person is the same for each call
E. No, the calls are ndependent, each one has two possibilities, but the probability of reaching live person is not the same for each call.