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

B Take a random sample of 3 tours and let $M=$ the amount of sales (in dollars) generated by the tours.
c Take a random sample of 30 tours and let $L=$ the number of tours that result in a sale.

Question

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

B Take a random sample of 3 tours and let $M=$ the amount of sales (in dollars) generated by the tours.
c Take a random sample of 30 tours and let $L=$ the number of tours that result in a sale.

Accepted Answer

∻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 $K$ 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 $M$ 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 $L$ 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.⚹◊What is the formula for calculating the expected value of a binomial random variable?⍭ Generate me a similar question◊

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