Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time in minutes for customers arriving during a 1-hour period. What is the probability that the total service time will exceed 2.5 hours?

Step-by-step explanation:

60 minutes = 1 hour

The statement would be

"Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per 60 minutes

If it takes approximately ten minutes to serve each customer, then the mean service time for in minutes for customers arriving during a 1-hour period is

10/60 × 7 = 1.67

In Poisson distribution, variance = mean

Therefore,

Variance = 1.67

The probability that the total service time will exceed 2.5 hours is expressed as P(x > 2.5)

Converting 2.5 hours to minutes, it becomes 2.5 × 60 = 150 minutes

From the Poisson distribution calculator,

P(x > 150) = 0

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

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step-by-step explanation: