Question

A soft drink company printed messages inside its? 20-ounce bottles as part of a promotion. Some of the caps said? “Please try? again!” while others? said, “”You’re a? winner!” The company claims that 1 in 6 bottles have winning caps. Seven friends each buy a bottle at a grocery store. The clerk is surprised when three of them win a prize. Is this group of friends just lucky or is the? company’s claim? inaccurate? Use simulation to estimate the probability of at least three of seven friends winning a prize.

Step? #1: Identify the component to be repeated.

A.

Winning a prize

B.

Buying one? 20-oz bottle

C.

Buying seven? 20-oz bottles

D.

The number of friends? (out of? 7) that receive? “You’re a? winner”

E.

The number of friends? (out of? 7) that receive? “Please try? again”

Step? #2: Explain how you could model the? component’s outcome.

A.

Let? 1-3 =? “You’re a? winner” and Let? 4-6 =? “Please try? again.”

B.

Let? 2-6 =? “You’re a? winner” and Let 1? = “Please try? again.”

C.

Let 0? = “Please try? again” and Let 1? = “You’re a? winner”

D.

Let 1? = “You’re a? winner” and Let? 2-6 =? “Please try? again.”

E.

Let 0? = “You’re a? winner” and Let 1? = “Please try? again”

Step? #3: State the response variable clearly.

A.

Buying one? 20-oz bottle

B.

Buying seven? 20-oz bottles

C.

Receiving? “Please Try? Again”

D.

Receiving? “You’re a? winner”

E.

The number of friends? (out of? 7) that receive? “You’re a? winner”

Step? #4: Explain how to combine the components into a trial to model the response variable.

A.

Use random.org to generate 7 random numbers between 1 and 6. Count and record the number of friends that receive? “Please try? again.”

B.

Use random.org to generate randomly selected numbers between 1 and 6 until three friends receive? “Your’re a? winner.”

C.

Use random.org to generate 7 random numbers between 1 and 6. Count and record the number of friends that receive? “You’re a? winner.”

D.

Use random.org to generate randomly selected numbers between 1 and 6 until three friends receive? “Please try? again.”

Step? #5: Run Several Trials

Use these random numbers provided listed below to carry out the simulation.

Trial? #1: ? 2 4 1 3 3 3 3

Trial? #2: ? 2 3 3 4 6 2 2

Trial? #3: ? 4 6 1 6 5 3 5

Trial? #4: ? 5 3 6 1 5 5 3

Trial? #5: ? 6 3 2 2 6 6 4

Trial? #6: ? 5 6 3 6 5 1 4

Trial? #7: ? 1 2 3 2 3 1 3

Trial? #8: ? 3 6 6 1 5 4 2

Trial? #9: ? 2 3 4 4 6 6 4

Trial? #10: ? 4 5 4 2 3 6 3

Trial? #11: ? 2 3 1 5 3 2 2

Trial? #12: ? 6 4 2 6 6 4 3

Trial? #13: ? 5 3 2 4 1 2 3

Trial? #14: ? 5 5 5 4 3 5 1

Trial? #15: ? 2 4 6 6 1 1 6

Trial? #16: ? 5 2 2 5 3 2 2

Trial? #17: ? 4 1 6 5 1 2 5

Trial? #18: ? 6 5 3 1 6 5 3

Trial? #19: ? 2 2 1 2 6 5 6

Trial? #20: ? 6 1 4 5 3 4 1

Step? #6: Collect and summarize the results of all trials.

Based on your? simulation, what is the probability of at least three of seven friends winning a? prize? Enter your final answer as a decimal rounded to FOUR decimal places.

0.12860.1286

Step? #7: State your conclusion

A.

The? company’s claim is inaccurate. The probability of at least three of seven friends winning a prize is so tiny that we have reason to question the? company’s claim.

B.

This group of friends is just lucky. The probability of at least three of seven friends is relatively? large, so we would expect to see this result on a pretty regular basis.

Answer 1

PARTS OF THE QUESTION ARE NOT WRITTEN PROPERLY. sO I CANNOT ANSWER THEM.

We will create a simulation to check. First, we will need to create a process that represents the situation. We could use a die and let a one be a winner and the other 5 numbers be try again. This allocation keeps the probability of success in any one repetition the same as the actual probability in the problem. Next we will roll the die seven times to see how many times we get a winner. We will repeat this process many times and calculate the number of times we get three winners out of seven people.

Finally we will use our results to make a claim. Let's say that getting three winners out of seven occurs 10% of the time. This result suggests that there is sufficient evidence to support the company's claim that 1-in-6 wins a prize.

7% OF THE TIME THERE ARE 3 WINNERS OUT OF 7 BY CHANCE

7 % IS NOT A SMALL NUMBER TO SAY THAT SODA COMPANY IS MISLEADING

Enter a random number in the calculator such as the student ID number or telephone number. Then press [STO->] [MATH] "PRB" "1:rand“. We want to pick 30 numbers, either 1 (let this represent tails) and 2 (heads). RandInt(1,2,30)" [ENTER].