For Problems #1 through #10, consider the following context:The coffee house chain Corner Caf operates some of itsretaillocations around the clock, twenty-four hours a day. The company's Chief Operations Officer, Maxine Venti, was wondering about the number of customers overnight between 2 AM and 5 AM. Letxrepresents the number of customers who made purchases during that time overnight at these open-all-night cafes at randomly selected locations on randomly selected dates. For example, 5% of these locations hadexactly zero(0) customers during this overnight time period on a specific date.

x	0	1	2	3	4	5	6	7	8
P(x)	5%	6%	?????	13%	21%	?????	15%	11%	?????

She forgot to enter two probabilities but recalls thator the chance that there were two customers overnight was exactly half the chance that there were exactly five customers overnight;also,she recalls that the probabilities ofeither nocustomersor eightcustomers making purchases at the kiosks overnight wereequally likely.Complete this probability distribution table and answer the following questions:[HINT:Express all answer as percentages using the percent symbol. Ex:1%or99%]

#1: Determine P(X = 2).

#2: Determine P (X = 5).

#3: Determine P (X= 8).

#4: Determine P ( X 4).

#5:What is the chance that a randomly selected 24-hour cafe did not have exactly seven (7) customers overnight making purchases?

#6: What is the chance that a randomly selected 24-hour cafe had either three (3) or four (4) customers overnight making purchases?

#7: What is the chance that a randomly selected 24-hour cafe had neither three (3) nor four (4) customers overnight making purchases?

#8: What is the chance that a randomly selected 24-hour cafe had no more than two (2) customers making purchases overnight?

#9:What is the chance that a randomly selected 24-hour cafe had at least five (5) customers making purchases overnight?

#10:On average, how many customers did these randomly selected 24-hour cafe have making purchases during these overnight hours? [HINTS: What is the expectation or expected value for this random variable? Express the answer rounded to the nearest whole number of customers. Enter only as a counting number: report approximately 8.49 customers only as 8, or approximately 9.50 customers only as 10.]