Questions: Homework Question 8, 3.2.25-T Part 5 of 6 HW Score: 95.51%, 12.42 of 13 points Points: 0.67 of 1 Save The accompanying data represent the weights (in grams) of a random sample of 48 MM plain candies. Complete parts (a) through (f). Click the icon to view the weights of the MM plain candies. (a) Determine the sample standard deviation weight. 0.036 gram(s) (Round to three decimal places as needed.) (b) On the basis of the accompanying histogram, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of MMs. A. The histogram is approximately bell-shaped so the Empirical Rule can be used. B. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used. C. The histogram is not approximately bell-shaped so the Empirical Rule can be used. D. The histogram is approximately bell-shaped so the Empirical Rule cannot be used. (c) Use the Empirical Rule to determine the percentage of MMs with weights between 0.803 and 0.947 gram. Hint: x̄=0.875. 95% (Type an integer or decimal. Do not round.) (d) Determine the actual percentage of MMs that weigh between 0.803 and 0.947 gram, inclusive. 95.8% (Round to one decimal place as needed.) (e) Use the Empirical Rule to determine the percentage of MMs with weights more than 0.911 gram. % (Type an integer or decimal. Do not round.) MM Candy Weights 0.87 0.90 0.91 0.86 0.90 0.93 0.87 0.88 0.91 0.88 0.88 0.87 0.86 0.84 0.82 0.84 0.89 0.88 0.88 0.86 0.87 0.90 0.81 0.83 0.83 0.94 0.92 0.89 0.93 0.86 0.84 0.86 0.91 0.91 0.82 0.84 0.89 0.93 0.84 0.84 0.88 0.95 0.86 0.85 0.79 0.91 0.88 0.87

Homework Question 8, 3.2.25-T Part 5 of 6 HW Score: 95.51%, 12.42 of 13 points Points: 0.67 of 1 Save The accompanying data represent the weights (in grams) of a random sample of 48 MM plain candies. Complete parts (a) through (f). Click the icon to view the weights of the MM plain candies. (a) Determine the sample standard deviation weight. 0.036 gram(s) (Round to three decimal places as needed.) (b) On the basis of the accompanying histogram, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of MMs. A. The histogram is approximately bell-shaped so the Empirical Rule can be used. B. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used. C. The histogram is not approximately bell-shaped so the Empirical Rule can be used. D. The histogram is approximately bell-shaped so the Empirical Rule cannot be used. (c) Use the Empirical Rule to determine the percentage of MMs with weights between 0.803 and 0.947 gram. Hint: x̄=0.875. 95% (Type an integer or decimal. Do not round.) (d) Determine the actual percentage of MMs that weigh between 0.803 and 0.947 gram, inclusive. 95.8% (Round to one decimal place as needed.) (e) Use the Empirical Rule to determine the percentage of MMs with weights more than 0.911 gram. % (Type an integer or decimal. Do not round.) MM Candy Weights 0.87 0.90 0.91 0.86 0.90 0.93 0.87 0.88 0.91 0.88 0.88 0.87 0.86 0.84 0.82 0.84 0.89 0.88 0.88 0.86 0.87 0.90 0.81 0.83 0.83 0.94 0.92 0.89 0.93 0.86 0.84 0.86 0.91 0.91 0.82 0.84 0.89 0.93 0.84 0.84 0.88 0.95 0.86 0.85 0.79 0.91 0.88 0.87
Transcript text: Homework Question 8, 3.2.25-T Part 5 of 6 HW Score: $95.51 \%, 12.42$ of 13 points Points: 0.67 of 1 Save The accompanying data represent the weights (in grams) of a random sample of $48 \mathrm{M} \mathrm{\& M}$ plain candies. Complete parts (a) through ( $f$ ). Click the icon to view the weights of the M\&M plain candies. (a) Determine the sample standard deviation weight. $0.036^{\prime} \operatorname{gram}(\mathrm{s})$ (Round to three decimal places as needed.) (b) On the basis of the accompanying histogram, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of M8Ms. A. The histogram is approximately bell-shaped so the Empirical Rule can be used. B. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used. C. The histogram is not approximately bell-shaped so the Empirical Rule can be used. D. The histogram is approximately bell-shaped so the Empirical Rule cannot be used. (c) Use the Empirical Rule to determine the percentage of M\&Ms with weights between 0.803 and 0.947 gram. Hint: $\bar{x}=0.875$. 95 \% (Type an integer or decimal. Do not round.) (d) Determine the actual percentage of M8Ms that weigh between 0.803 and 0.947 gram, inclusive. $95.8 \%$ (Round to one decimal place as needed.) (e) Use the Empirical Rule to determine the percentage of M\&Ms with weights more than 0.911 gram. $\square$ \% (Type an integer or decimal. Do not round.) M\&M Candy Weights \begin{tabular}{|llllllll|} \hline 0.87 & 0.90 & 0.91 & 0.86 & 0.90 & 0.93 & 0.87 & 0.88 \\ 0.91 & 0.88 & 0.88 & 0.87 & 0.86 & 0.84 & 0.82 & 0.84 \\ 0.89 & 0.88 & 0.88 & 0.86 & 0.87 & 0.90 & 0.81 & 0.83 \\ 0.83 & 0.94 & 0.92 & 0.89 & 0.93 & 0.86 & 0.84 & 0.86 \\ 0.91 & 0.91 & 0.82 & 0.84 & 0.89 & 0.93 & 0.84 & 0.84 \\ 0.88 & 0.95 & 0.86 & 0.85 & 0.79 & 0.91 & 0.88 & 0.87 \\ \hline \end{tabular
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Solution

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Solution Steps

Step 1: Sample Standard Deviation

The sample standard deviation is already given in the problem as 0.036 grams.

Step 2: Appropriateness of Empirical Rule

The histogram appears roughly bell-shaped. Therefore, the Empirical Rule can be used.

Step 3: Percentage of M&Ms within given range using Empirical Rule

The Empirical Rule states that for a bell-shaped distribution:

  • Approximately 68% of the data falls within one standard deviation of the mean.
  • Approximately 95% of the data falls within two standard deviations of the mean.
  • Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean (\(\bar{x}\)) is 0.875 and the standard deviation (s) is 0.036, we want to find the percentage of M&Ms with weights between 0.803 and 0.947.

Lower bound: 0.875 - 2 * 0.036 = 0.803 Upper bound: 0.875 + 2 * 0.036 = 0.947

Since the range 0.803 to 0.947 is two standard deviations from the mean, according to the Empirical Rule, approximately 95% of the M&Ms fall within this weight range.

Final Answer

(a) \( \boxed{0.036} \) (b) \( \boxed{A} \) (c) \( \boxed{95} \)

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