Question

A small cafeteria has a single coffee-making machine. There can be delays if several customers all want coffee at the same time. The proprietor has observed that on average 60% of customers want coffee from the machine.

nonconforming.

(a) If six customers enter the cafeteria, what is the probability distribution for the number of customers, X, who will want coffee from the machine?

(b) What is the probability that at least four of the six customers will want coffee from the machine?

(c) Explain what the assumption of independence means in this context, and suggest a possible reason for non-independence in this situation.      

Answer 1

Ans:

a)X has binomial distribution with n=6 and =0.60

b)

P(x=k)=6Ck*0.60^k*0.40^6-k

x	P(x)
0	0.0041
1	0.0369
2	0.1382
3	0.2765
4	0.3110
5	0.1866
6	0.0467

P(at least 4)=P(X>=4)

=P(x=4)+P(x=5)+P(x=6)

=0.3110+0.1866+0.0467

=0.5443

c)Assumption of independence means that outcome of one trial does not affect the outcome of other trial.

As,One customer's choice to have coffee may affect other customers,so it is a possible reason for non-independence in this situation.