A bar is trying to get a feel for the number of drinks that a person will order. Let the random variable X

denote the number of drinks a customer will buy. From past experience the bar knows that 20% of

people will order 1 drink, 30% will order 2 drinks, 30% order 3 drinks, and10% order 4 drinks. If a

customer may buy anywhere from 0 to 4 drinks then answer the following questions.

a) Create a probability distribution for X and make a probability histogram.

b) How many drinks should the bar expect people to purchase?

c) Find the standard deviation of the distribution and interpret its meaning.

d) Find the probability that a customer orders one or more drinks.

e) What is the probability that a customer will purchase at least 1 drink if we know they will

purchase less than 3 drinks?

Tom works the night shift at a gas station. From past experience, Tom knows that 80% of all customers who purchase gas pay at the pump with a credit card. Assume that customers either pay at the pump with a credit card or not, independently of each other. One evening 15 customers arrive at the gas station and Tom counts the number of them that pay with a credit card.

a) Define a random variable for this problem and state its distribution and parameters.

b) Out of 15 customers who purchase gas, how many should Tom expect to pay at the pump with a credit card?

c) What is the probability that exactly 10 customers out of 15 pay at the pump with a credit card?

d) What is the probability that at least 9 customers out of 15 pay at the pump with a credit card?

e) What is the probability that the number of customers purchasing gas with a credit card is somewhere from 3 to 12 customers?