Question 1
A small grocery store has two checkout lines available to its customers: a regular checkout line and an express checkout line. Customers with 5 or fewer items are expected to use the express line. Let X and Y be the number of customers in the regular checkout line and the express checkout line, respectively. Note that these numbers include the customers being served, if any. The joint probability distribution of Xand Yis given in the table below.
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Y = 0
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Y=1
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Y=2
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3
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X = 0
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0.06
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0.04
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0.03
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0.15
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X =1
|
0.09
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0.06
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0.03
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0.04
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X=2
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0.08
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0.05
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0.01
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0.12
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3
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0.07
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0.05
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0.03
|
0.09
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The marginal distribution of X when P(x=0) is Blank 1 . The marginal distribution of Y when P(y=0) is Blank 2 . The conditional probability of X given Y, where X =2 and Y =2. is equal to Blank 3 .
If we find that the probability that customers are waiting in the regular line when the express line is empty is relatively large, we might permit some customers in the regular line to switch to the express line when it is empty. Conversely, if we learn that the probability that no customers are waiting in the regular line when the express line is busy is relatively large, we might then encourage express line customers to switch to the idle regular line. The idea here is to reduce the average waiting time of the customers.
The probability that no one is waiting or being served in the regular checkout line is Blank 4 .
On average, the eexpected number of customers in regular line =E(X) = Blank 5 , and the expected number of customers in express line =E(Y) =Blank 6
Question 2
The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. For this question, enter all probabilities s a point digit with 4 point digits, for example the answer should be like 0.1264 not like 12.64% or 13%.
What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?
What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?
What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
What is the probability that between three and six (exclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?