M\&M's come in many colors. It is claimed that $$ 10 \% $$ of the candies are green and that bags are packed randomly. Suppose that the candies are packed a) If we plot a histogram showing the proportions of green candies in the various bags, what shape would you expect it to have? A. A skewed right shape B. A skewed left shape C. An approximately Normal shape D. The shape cannot be determined. b) Can the histogram be approximated by a Normal model? Explain. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or decimal rounded to one decimal place as needed.) A. Yes. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the candies are chosen randomly, and the $$ 10 \% $$ Condition is met since np $$ =\square \geq 10 $$ and $$ n q=\square \geq 10 $$. B. No. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the candies are chosen randomly, but the $$ 10 \% $$ Condition is not met since nq $$ =\square

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M\&M's come in many colors. It is claimed that $$ 10 \% $$ of the candies are green and that bags are packed randomly. Suppose that the candies are packed a) If we plot a histogram showing the proportions of green candies in the various bags, what shape would you expect it to have? A. A skewed right shape B. A skewed left shape C. An approximately Normal shape D. The shape cannot be determined. b) Can the histogram be approximated by a Normal model? Explain. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or decimal rounded to one decimal place as needed.) A. Yes. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the candies are chosen randomly, and the $$ 10 \% $$ Condition is met since np $$ =\square \geq 10 $$ and $$ n q=\square \geq 10 $$. B. No. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the candies are chosen randomly, but the $$ 10 \% $$ Condition is not met since nq $$ =\square<10 $$. C. No. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the

UpStudy AI · Accepted Answer

a) The histogram of the sample proportions will be approximately Normal.

b) We can use a Normal model provided the conditions for a binomial distribution are met. For a binomial with parameters $$ n $$ and $$ p=0.10 $$, we need both
$$
np\ge10 \quad \text{and} \quad nq\ge10,
$$
where $$ q=1-p=0.90 $$. If, for example, a bag contains $$ n=100 $$ candies then
$$
np=100(0.10)=10 \quad \text{and} \quad nq=100(0.90)=90.
$$
Thus, both conditions are satisfied.

So the correct answer is:

**A. Yes. The Independence Assumption is met since the candies are independent of each other, the Randomization Condition is met since the candies are chosen randomly, and the $$ 10\% $$ Condition is met since $$ np=10\ge10 $$ and $$ nq=90\ge10 $$.**
a) The histogram will have an approximately Normal shape. b) Yes, the histogram can be approximated by a Normal model because the Independence Assumption, Randomization Condition, and the $$ 10\% $$ Condition are all met.

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