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Question
Math
Posted 8 months ago

Ravi sells real estate. Based on previous data, he knows that 5%5 \% 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 3 tours and let K=K= the number of tours that result in a sale.

B Take a random sample of 3 tours and let M=M= the amount of sales (in dollars) generated by the tours.
c Take a random sample of 30 tours and let L=L= the number of tours that result in a sale.
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Answer from Sia
Posted 8 months ago
Solution by Steps
step 1
Identify the characteristics of a binomial random variable
step 2
A binomial random variable must satisfy the following conditions: there are a fixed number of trials (n), each trial has only two possible outcomes (success or failure), the probability of success (p) is the same for each trial, and the trials are independent
step 3
Evaluate Option A: Taking a random sample of 3 tours and letting KK be the number of tours that result in a sale. This situation has a fixed number of trials (3), two possible outcomes (sale or no sale), a constant probability of success (5%), and the trials are independent
step 4
Evaluate Option B: Taking a random sample of 3 tours and letting MM be the amount of sales (in dollars) generated by the tours. This does not fit the binomial criteria because the amount of sales in dollars is not a count of successes or failures
step 5
Evaluate Option C: Taking a random sample of 30 tours and letting LL be the number of tours that result in a sale. This situation also has a fixed number of trials (30), two possible outcomes (sale or no sale), a constant probability of success (5%), and the trials are independent
Answer
Options A and C are binomial random variables.
Key Concept
Binomial Random Variable
Explanation
A binomial random variable must have a fixed number of independent trials, each with the same probability of success, and only two possible outcomes. Options A and C meet these criteria.

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