Question

For which of the following settings might it be reasonable to use a binomial distribution to describe the random variable X?

X is the number of calls received by GE's appliance service center per hour on Mondays through Fridays between 8:00 A.M. and 5:00 P.M.
	X is the number of ounces of soda dispensed by a machine into 10-ounce cups.
	A company has 250 employees. A random sample of 50 of the employees is taken. X is the number of employees in the sample who called in sick at least once last month.
	X is the number of consumers in a sample of 250 who prefer Apple computers to PCs.

Answer 1

For binomial distribution, the trials should be independent of each of other and the probability of success in each trial should be equal and independent of each other.

a) The number of calls received is a case of a poisson distribution, as there are no trials here. (Binomial distribution is a sum of bernoulli trials, but there are no trials here. )

b) Again, here we are modelling the number of arrivals like distribution and is therefore again a poisson distribution and not a binomial.

c) The number of employees in the sample of 50 employees who called in sick can be modelled here as

Where p is the probability of an employee calling in sick at least once a month. (This prob. being independent of others ) . Therefore this is a case of a binomial distribution here.

d) The number of consumers in the sample who prefer Apple computers to PCs can be modelled as a binomial distribution where the probability parameter p would be the probability of a person preferring Apple to PCs.

Therefore this is also a binomial distribution here.