For the following problems show your 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). Use the table or normal approx. whenever they are appropriate. When using normal approx., remember to check all conditions and remember your answer is only an approximation!

30% of OSU students have cars that are black. Suppose you randomly sample 5 OSU students, and let X be the number of students in the sample with black cars. Find the probabilities of the following events.
Exactly 3 students in the sample have black cars.
More than 3 students in the sample have black cars.
Between 1 and 4 students (inclusive) in the sample have black cars.
Less than half of the students in the sample have black cars.
At least one student in the sample has a black car.
There are two conditions that you have to check before using the normal approximation when X is binomial.
Write down the two conditions.
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.)
Suppose it is reported that 10% of OSU business students major in international marketing. You sample 200 OSU business students at random. Let X = the number of students in the sample who major in international marketing.
How many students in your sample do you EXPECT to major in int’l marketing, according to the above information?
What is the probability that your sample finds that at least 15 students major in international marketing?
Are your findings typical of what you EXPECTED to get? Why or why not? (Think about your answers to parts a and b.)
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.
Is the distribution of the number of unsatisfied customers from this sample binomial? Justify.
What is the probability that 5 customers are unsatisfied?
USING THE FORMULA AND THE TABLE TO VERIFY: What is the probability that at most 2 customers are unsatisfied? Show your work.