Question

Math

Posted 3 months ago

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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.
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Identify the characteristics of a binomial random variable

step 2

A binomial random variable must have a fixed number of trials, two possible outcomes (success or failure), constant probability of success on each trial, and independence between trials

step 3

Evaluate option A: A random sample of 3 tours with $K=$ the number of tours that result in a sale. This scenario has a fixed number of trials (3), two outcomes (sale or no sale), constant probability of success (5%), and independence is assumed

step 4

Evaluate option B: A random sample of 3 tours with $M=$ the amount of sales (in dollars). The amount in dollars is not a count of successes or failures, so it does not fit the criteria for a binomial random variable

step 5

Evaluate option C: A random sample of 30 tours with $L=$ the number of tours that result in a sale. This scenario also has a fixed number of trials (30), two outcomes (sale or no sale), constant probability of success (5%), and independence is assumed

1 Answer

Options A and C are binomial random variables.

Key Concept

Binomial Random Variable

Explanation

A binomial random variable must satisfy four conditions: a fixed number of trials, two possible outcomes for each trial, a constant probability of success, and independence between trials. Options A and C meet these criteria, while option B does not because it involves a continuous outcome (amount in dollars) rather than a count of successes or failures.

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