1.) The standard deviation of a binomial probability distribution with n trials and probability p of success is: a. np b. square root of (np(1-p)) c. n + p d. np(1-p)

2.) f 30% of Americans own a pet and you select 100 Americans at random and let X = number who own a pet. What is the mean and standard deviation of X?

For the following problems show work, and make sure you use probability notation in your work. For example, if trying to find the probability that X is greater than 2 write: P(X>2)

3.) There are two conditions that you have to check before using the normal approximation when X is binomial. a. Write down the two conditions. b. Why do we have to check BOTH conditions rather than just one, to be able to use the normal approximation? (Including an example with your explanation is OK.)

4.) Suppose 20% of a bank's customers report being unsatisfied. You take a sample of 20 customers at random and count the number of unsatisfied customers. a. Is the distribution of the number of unsatisfied customers from this sample binomial? Justify. b. What is the probability that 5 customers are unsatisfied? c. USING THE FORMULA AND THE TABLE TO VERIFY: What is the probability that at most 2 customers are unsatisfied? Show your work.

5.) Suppose we have a 20 question MCTF test where each question has 4 possible answers. a. If you guess on all the questions, and you let X be the number you get right, what is the mean of X? Why does this number make sense?

b. If you guess on all the questions, and you let X bet the number you get right, what is the standard deviation of X? c. If someone got 10 questions right on this test, do you think they were guessing? Why or why not? Use the binomial table to help you decide.

6.) Suppose 30% of OSU students watch reality TV shows of some kind every week. Ten OSU students are selected at random and asked if they watch reality TV of some kind each week. You want the probability that at least 4 of them say yes. a. What does X represent in this problem? b. Show BRIEFLY that X has a binomial distribution. c. Find the probability that at least 4 of the students say yes. d. Could a person use the normal approximation to answer this question? Explain briefly.