Janet makes 67% of free throws in her basketball games. Her coach wants to know the probability that she will make 7 out of the next 8 free throws.

Which simulation design has an appropriate device and a correct trial?

To determine the probability that Janet will make 7 out of the next 8 free throws, we can use a binomial distribution simulation.

The appropriate device for this simulation would be a computer or calculator that can generate random numbers between 0 and 1.

The correct trial for this simulation would be to simulate a large number of trials, where each trial represents Janet attempting 8 free throws. In each trial, we would simulate the outcome of those 8 free throws using her known free throw percentage of 67%.

Here's how you can perform this simulation to estimate the probability:

1. Set up a loop to simulate a large number of trials, such as 10,000 or more. Let's call this loop "trial".

2. Inside the "trial" loop, set up another loop to simulate the outcome of 8 free throws. Let's call this loop "throw".

3. Inside the "throw" loop, generate a random number between 0 and 1 using the appropriate device mentioned earlier.

4. Compare the generated random number with Janet's free throw percentage. If the random number is less than or equal to 0.67, count it as a made free throw. Otherwise, count it as a missed free throw.

5. Repeat steps 3 and 4 eight times to simulate the outcome of all 8 free throws in the "throw" loop.

6. After the "throw" loop, check if the count of made free throws is equal to 7. If it is, increment a counter for successful trials. Otherwise, do nothing.

7. Repeat steps 2 to 6 in the "trial" loop until all trials are completed.

8. Calculate the probability by dividing the number of successful trials by the total number of trials.

By running this simulation and increasing the number of trials, you should obtain a more accurate estimation of the probability that Janet will make 7 out of the next 8 free throws based on her known free throw percentage of 67%.

k = make , s = miss

this is a binomial probability ...(k + s)^8

the 2nd term is ... 8 k^7 s ... p = 8 * .67^7 * .33