Question

Ravi sells real estate. Based on previous data, he knows that 5% percent of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply:

A) Take a random sample of 333 tours and let K=K=K, equals the number of tours that result in a sale.
B) Take a random sample of 333 tours and let M=M=M, equals the amount of sales (in dollars) generated by the tours.
C) Take a random sample of 303030 tours and let L=L=L, equals the number of tours that result in a sale.

Answer 1

In the listed scenarios, choice A and C represent binomial random variables because they count the number of sales (successes) in a fixed number of independent trials (tours) with a constant probability of success. Choice B is not a binomial random variable because it measures sales in dollars, not the count of successes.

Step-by-step explanation:

The student's question involves understanding which scenarios describe a binomial random variable. A binomial random variable must have a fixed number of independent trials, only two outcomes (success or failure), a constant probability of success, and the variable measured is the number of successes.

• A) Taking a random sample of 333 tours and letting K equal the number of tours that result in a sale fits the criteria for a binomial random variable, as each tour is an independent trial with a success (sale) or failure (no sale), a fixed number of trials (333), and a constant probability of success (5%).
• B) Taking a random sample of 333 tours and letting M equal the amount of sales (in dollars) is not a binomial variable since the outcome is not binary (it is a dollar amount rather than a count of successes).
• C) Taking a random sample of 30 tours and letting L equal the number of tours that result in a sale also meets the criteria of a binomial random variable.