Chapter 5, Problem T5.5SPT

To determine

To find out which of the following is a correct way to perform the simulation.

Answer to Problem T5.5SPT

Option (c) is the correct option.

Explanation of Solution

In the question we have to find out the correct way to perform the simulation. Thus, we are interested in simulation where the person has a $56\%$ probability of make a free throw while estimating the probability of making $34$ or more free throws in a sample of $50$ throws. Since we are require a $56\%$ probability to make a free throw then, $56\text{ among 100}$ numbers should corresponds with making a free throw. We then note that we require that the integers $1\text{ to 56}$ represent making a free throw and that the integers $57\text{ to 100}$ represents missing a free throw. This then corresponds with the options (c) and (d). Thus, one of these two options will be correct option.

The difference between answer options (c) and (d) is that (c) allows repetitions of the randomly selected integers and (d) does not allow repetitions of the randomly selected integers. In this case, repetitions should be allowed because if you do not allow repetitions, then the probability of making a free throw will no longer be $56\%$ after the first free throw. This then implies that (c) is the correct option.