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A study of the checkout lines at the Safeway Supermarket
Chapter 6, Problem 51E(choose chapter or problem)
Problem 51E
A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find:
a. No customers are waiting?
b. Four customers are waiting?
c. Four or fewer are waiting?
d. Four or more are waiting?
Questions & Answers
QUESTION:
Problem 51E
A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find:
a. No customers are waiting?
b. Four customers are waiting?
c. Four or fewer are waiting?
d. Four or more are waiting?
ANSWER:
Solution :
Step 1 of 4:
Let X denote the number of customers waiting during the rush hour.
Let X follows a Poisson distribution with parameter 4.
Then the Poisson distribution formula is
P(X=x) =
Where 3.
P(X=x) =
Our goal is:
a). We need to find the probability that no customers are waiting.
b). We need to find the probability that 4 customers are waiting.
c). We need to find the probability that 4 or fewer customers are waiting.
d). We need to find the probability that 4 or more customers are waiting.
a). The probability of no customers is waiting is
P(X=x) =
Where x=0.
P(X=0) =
P(X=0) =
P(X=0) = 0.04978
Therefore, the probability of no customers are waiting is 0.04978.