Question

For which of the following situations would a binomial distribution not be a reasonable probability model for the random variable?

Question 1 options:

	A car rental company is interested in the color (red, green, grey, black, or white) of car that customers prefer to rent. The random variable, x, is the color of car selected by the customer.
	A researcher is interested in the gender of babies born at a specific hospital. The researcher plans to observe the next 50 births and record the gender. The random variable, x, is the number of girls born among the 50 observed.
	A researcher observes the group of patients who received an experimental drug. The random variable, x, is the number of patients who had an undesirable side effect.
	A manufacturer of lamps is interested in the number of lamps produced that are faulty so he randomly selects 75 lamps and tests whether or not they function correctly. The random variable, x, is the number of lamps that do not work properly.
	All of the above are binomial distributions.

Answer 1

The correct answer is:

A car rental company is interested in the color (red, green, grey, black, or white) of car that customers prefer to rent. The random variable, x, is the color of car selected by the customer.

Here the random variable can take values - red, green, grey, black, or white. This is a categorical variable and thus a binomial distribution will not be a reasonable probability model for the random variable.

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