The mean number of customers arriving at a restaurant during a 15-minute period is 8. Find the probability that at least 4 customers will arrive at the restaurant during a 15-minute period.
Given :
The mean number of customers arriving at a restaurant during a 15-minute period is 8.
Mean =
= 8
Let X be the number of customers will arrive at the restaurant during a 15-minute period.
X follows the Poisson distribution with parameter
= 8.
X ~ Poisson (=8)
The probability density function of Poisson distribution is given by
P(X=x) = e^-
*
^x /X!
The probability that at least 4 customers will arrive at the restaurant during a 15-minute period :
P(X4)
= 1 - P(X < 4)
= 1 -
e^-8 * 8^x /X!
= 1 - 0.0424
= 0.9576
Therefore the probability that at least 4 customers will arrive at the restaurant during a 15-minute period is 0.9576
The mean number of customers arriving at a restaurant during a 15-minute period is 8. Find...
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