Question

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent poll, $75\%$ of American adults regularly recycle. To simulate choosing a random sample of $100$ U.S. adults and seeing how many

of them recycle, roll a $4$-sided die $100$ times. A result of $1,2$, or $3$ means the person recycles; a $4$ means that the person doesn’t recycle.

(b) An archer hits the center of the target with $60\%$ of her shots. To simulate having her shoot $10$ times, use a coin. Flip the coin once for each of the 10

shots. If it lands heads, then she hits the center of the target. If the coin lands tails, she doesn’t.

Short answer

Part (a) It is valid.

Part (b) It is not valid.

Step-by-step solution

Part (a) Step 1. Given Information  

The simulation designs are available for download. It is necessary to determine what is wrong with each of them.

Part (a) Step 2. Concept Used   

A simulation is a method of simulating random behaviour using a model that accurately reflects the circumstance, which is usually done with random numbers.

Part (a) Step 3. Explanation  

The simulation in the question is accurate. It's valid since the person recycles if they roll a $1,2$, or $3$, which corresponds to $3$ of the $4$ possible outcomes. As a result, $\frac{3}{4}=0.75=75\%$ is implied. As a result, the simulation depicts a sample of people who recycle 75% at the time.

Part (b) Step 1. Explanation   

The simulation in the question isn't accurate. Because the coin has a$50\%$ probability of landing heads vs a $60\%$chance of reaching the goal, this is not a credible simulation. As a result, the simulation presented is invalid.