A barbershop averages 5 customers per hour between 12:00 noon and 5:00 pm. Let X

Question

A barbershop averages 5 customers per hour between 12:00 noon and 5:00 pm. Let X be the number of customers arriving between 2:00 pm and 3:00 pm. What is the distribution of X? That is, write down the name of the distribution and also give the parameter value 1. 2. What is the probability that exactly 6 customers will arrive between 2:00 pm and 3:00 pm on Wednesday? 3. What are the mean and the standard deviation of x? Suppose that we will record the number of customers arriving between 2:00 pm and 3:00 pm over a 7-day period. Assume the numbers of customers on different days are independent. Let Y be the number of days with exactly 6 customers. What is the distribution of Y? That is, write down name of the distribution and give the parameter values. 4. 5. Evaluate Pr(Y-1Y2 1). 6. Evaluate the mean and the standard deviation of Y

Explanation / Answer

1) X follows poisson distribution with parameter lambda=5

As there is only 1 hour between 2 and 3 pm

2)

P(x=6)

=e^(-5)*5^6/6!

=0.14622

3) mean = lambda=5

Sd=sqrt(lambda) =sqrt(5)

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