A firm is considering using the Internet to supplement its traditional sales met

Question

A firm is considering using the Internet to supplement its traditional sales methods. Using data from an industry association, the firm estimates that 1 of every 1,000 Internet hits results in a sale. Suppose the firm has 2, 500 hits per day. What is the probability that the firm will have more than five sales in a randomly selected day? What conditions must be satisfied in order for you to make the calculation in part(a)? Use the Poisson approximation to compute the probability that the firm will have more than five sales in a randomly selected day. Is the Poisson approximation accurate?

Explanation / Answer

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
it is given that 1 in evevry 1000 results in a sale
we have 2500 hits per day and the mean rate is can be calculated to = 2500/1000 = 2.5
a.
P( X = 5 ) = e ^-2.5 * 2.5^5 / 5! = 0.0668

b.
the mean rate should be consistant across all the days
c.
P( X < = 5) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-2.5 * 2.5 ^ 5 / 5! + e^-2.5 * 0 ^ 4 / 4! + e^-2.5 * ^ 3 / 3! + e^-2.5 * ^ 2 / 2! + e^-2.5 * ^ 1 / 1! + e^-2.5 * ^ 0 / 0!
= 0.958
P( X > 5) = 1 -P ( X <= 5) = 1 - 0.958 = 0.042

d.
yes, it is accurate, since the value of the 'N' is unknnown

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