Question

In: Statistics and Probability

A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.

(a) Construct the distribution for the random variable X?

(b) Find the mean and standard deviation of X.

(c) What is the probability that the time between consecutive arrivals (customers) will fall between 3 and 6 minutes?

Expert Solution

Let Y be the number of customers arrived between 8:00 am to 9:00 am
Here Y~Poisson(12)

Here, X represent the time between arrivals.




.....................(i)
Now,

a) The Distribution of X is:

b) Mean and Standard Deviation:



   [as,]

Now, we are to calculate:






Standard Deviation: S.D.(X)

Mean=

S.D.=0.1443

c)Here we're asked to calculate:

[from equation (i)]

orchestra answered 2 years ago

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