Questions: The accompanying data represent the weights (in grams) of a random sample of 48 MM plain candies. Complete parts (a) through (d). (a) Determine the sample standard deviation weight. 0036 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 cannot be used. B. The histogram is not approximately bell-shaped so the Empirical Rule can be used. C. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used. D. The histogram is approximately bell-shaped so the Empirical Rule can 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. % (Round to one decimal place as needed.) 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 0.85 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

The accompanying data represent the weights (in grams) of a random sample of 48 MM plain candies. Complete parts (a) through (d).

(a) Determine the sample standard deviation weight.
0036 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 cannot be used.
B. The histogram is not approximately bell-shaped so the Empirical Rule can be used.
C. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used.
D. The histogram is approximately bell-shaped so the Empirical Rule can 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. 
% (Round to one decimal place as needed.)

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 0.85 
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: The accompanying data represent the weights (in grams) of a random sample of 48 M&M plain candies. Complete parts (a) through (d). (a) Determine the sample standard deviation weight. 0036 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 M&Ms. A. The histogram is approximately bell-shaped so the Empirical Rule cannot be used. B. The histogram is not approximately bell-shaped so the Empirical Rule can be used. C. The histogram is not approximately bell-shaped so the Empirical Rule cannot be used. D. The histogram is approximately bell-shaped so the Empirical Rule can be used. (c) Use the Empirical Rule to determine the percentage of M&Ms with weights between 0.803 and 0.947 gram. Hint: $\overline{\mathrm{x}}=0.875$. 95 \% (Type an integer or decimal. Do not round.) (d) Determine the actual percentage of M&Ms that weigh between 0.803 and 0.947 gram, inclusive. \% (Round to one decimal place as needed.) 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 & 0.85 \\ 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: Determine the sample standard deviation weight

The sample standard deviation weight is given as 0.036 grams, rounded to three decimal places.

Step 2: Comment on the appropriateness of using the Empirical Rule

The histogram is approximately bell-shaped, so the Empirical Rule can be used. This is indicated by option D.

Step 3: Use the Empirical Rule to determine the percentage of M&Ms with weights between 0.803 and 0.947 grams

Using the Empirical Rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the percentage of M&Ms with weights between 0.803 and 0.947 grams is 95%.

Final Answer

  1. Sample standard deviation weight: 0.036 grams
  2. The histogram is approximately bell-shaped, so the Empirical Rule can be used.
  3. Percentage of M&Ms with weights between 0.803 and 0.947 grams: 95%
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