Question

A travelling salesman sells milkshake mixing machines and on average sells 8.4 machines per month. He needs to sell at least 3 machines each month order to stay in business, otherwise he will shut down. Determine the probability distribution used in this class which might appropriately be used to approximate the distribution of machine sales. What is the probability he will have to shut down after this month, i.e., sell fewer than 3 machines

Answer 1

P(X<3) = 0.01004

Explanation:

From the given information:

Consider the application of Poisson distribution
`P(X = x ) = (e^(-\lambda) \lambda ^x)/(x!)` with the parameter
`\lambda = 8.4`;

Therefore, we can calculate the required probability as follows:

P(X< 3) = P(X = 0) + P(X = 1) + P(X =2)

`P(X< 3) = (e^(-8.4) 8.4^0)/(0!) + (e^(-8.4) 8.4^1)/(1!) + (e^(-8.4) 8.4^2)/(2!)`

`P(X< 3) =e^(-8.4)( 1 + 8.4+35.28)`

P(X<3) = 0.01004