Customers make purchases at a convenience store, on average,
every ten and half minutes. It is fair to assume that the time
between customer purchases is exponentially distributed. Jack
operates the cash register at this store.
a-1. What is the rate parameter λ? (Round
your answer to 4 decimal places.)
a-2. What is the standard deviation of this
distribution? (Round your answer to 1 decimal
place.)
b. Jack wants to take a nine-minute break. He
believes that if he goes right after he has serviced a customer, he
will lower the probability of someone showing up during his
nine-minute break. Is he right in this belief?
Yes
No
c. What is the probability that a customer will
show up in less than nine minutes? (Round intermediate
calculations to at least 4 decimal places and final answer to 4
decimal places.)
d. What is the probability that nobody shows up
for over forty minutes? (Round intermediate calculations to
at least 4 decimal places and final answer to 4 decimal
places.)
ANSWER:-
Rate parameter λ :
The standard deviation of this distribution : eleven and half minute.
The probability that a customer will show up in less than seven minutes :
Since times between purchases are exponentially distributed with
average of eleven and half minute , the distribution is given
by
P( T < t) = 1 - e^(-t/11.5), and you want t = 7, so, P(T < 7)
= 1 - e^(7/11.5)
Probability that nobody shows up for over forty-five minutes :
P( T > 45) = e^(-45/6) = 1808.0424
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