1. Determine whether the random variable below satisfies the conditions for a binomial setting, a geometric setting, or neither (you don't need to actually calculate the number). Support your conclusion (is there an acronym you can use...?)

Suppose that one out of every 300 squirrels in a large forest is born with white fur. As a collector of exotic animals you'd like to find a white squirrel to add to your menagerie. How many squirrels would you expect to have to catch in order to find the first squirrel who has white fur?

2. Ricky runs a hamburger stand by the beach. He estimates that 40% of his customers order their hamburger with cheese. Let's assume that Ricky's estimate is accurate and the odds are independent, and we select 20 customers at random from his hamburger stand.

a) Determine the probability that exactly 7 of the 20 get cheese on their burger.

b) Find the probability that more than 9 customers out of 20 get cheese on their burger.

c) What is the probability that fewer than 6 customers get cheese on their burger?

3. An online store gives away a t-shirt with every purchase. 25% of the shirts are red and 75% are blue, and each customer receives one shirt per purchase chosen at random.

a) How many purchases on average would you have to make to get your first red ribbon?

b) If you make 4 purchases, what is the probability you get at least 1 red ribbon?

c) If you make two purchases, what is the probability that you get one red and one blue ribbon?

4. Mariela runs a small side business making fleece vests for dogs (so cute!). Using data from past years, she estimates the amount she'll sell in any given month is Normally distributed with a mean of $470 and a standard deviation of $58. The monthly cost of buying materials is also Normally distributed, with a mean of $300 and a standard deviation of $45. What is the probability that Mariela makes a profit of at least $250 in a random month?

5. In a chocolate factory, 30% of all chocolates made contain caramel in the center.

(a) What is the probability that you must sample exactly 6 chocolates to find the first one that is caramel?

(b) What is the probability that you must sample 5 or more chocolates to find the first one that is a caramel?

6. A company that rents DVDs from vending machines in grocery stores has developed the following probability distribution for the random variable X = the number of DVDs a customer rents per visit to a machine.

X

1

2

3

4

P(X)

0.5

0.3

0.1

0.1

a) Find and interpret the mean (expected value) of X.

b) Find and interpret the standard deviation of X.

c) What is the probability that a customer rents more than 2 DVDs per visit to a machine?