1) A variable X has a uniform distribution on the interval from 4 to 22. What is the interquartile range of the distribution of X?

2)The manager of a gas station and convenience store tabulates the following facts:

• 60% of customers purchase gasoline (G).
• 37% of customers purchase cigarettes (C).
• 74% of customers purchase gasoline or a drink (D).
• 17% of customers purchase gasoline and cigarettes. 
• 21% of customers purchase a gasoline and a drink.
• 15% of customers purchase cigarettes and a drink. 
• 2% of customers purchase all three items.

(a)  If we randomly select a customer, what is the probability that she purchases gasoline or cigarettes?  

(b)  If we randomly select a customer, what is the probability that she purchases a drink? 

(c)  Are any of the pairs of events independent of one another?  Explain.

(d)  Are any of the pairs of events mutually exclusive?  Explain.

(e)  What is P(C  D^c), i.e., the probability that a randomly selected customer purchases cigarettes but not a drink?3)

Suppose we have two bowls full of candies.  Each bowl contains four different flavours of candy - grape (which are purple), lemon (which are yellow), cherry (which are red) and raspberry (which are also red). 

(a)  What is the probability that the first selected candy is lemon or that the second selected candy is cherry? 

(b)  Let X be the number of grape candies that are selected.  Find the probability distribution of X :