Math Problem Statement

The accompanying data represent the weights​ (in grams) of a random sample of 48​ M&M plain candies. Complete parts​ (a) through​ (f). 0.87 0.91 0.89 0.83 0.91 0.88 0.90 0.88 0.88 0.94 0.91 0.95 0.91 0.88 0.88 0.92 0.82 0.86 0.86 0.87 0.86 0.89 0.84 0.85 0.90 0.86 0.87 0.93 0.89 0.79 0.84 0.90 0.93 0.91 0.87 0.82 0.81 0.84 0.84 0.88 0.88 0.85 0.84 0.83 0.90 0.86 0.84 0.87 ​(a) Determine the sample standard deviation weight. ​(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. ​(c) Use the Empirical Rule to determine the percentage of​ M&Ms with weights between 0.804 and 0.944 gram.​ Hint: x overbar equals 0.874 . ​(d) Determine the actual percentage of​ M&Ms that weigh between 0.804 and 0.944 ​gram, inclusive. (e) U se the Empirical Rule to determine the percentage of​ M&Ms with weights more than 0.909 gram. ​(f) Determine the actual percentage of​ M&Ms that weigh more than 0.909 gram.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Empirical Rule
Standard Deviation
Normal Distribution

Formulas

Sample Standard Deviation formula: s = sqrt[ Σ(xi - x̄)² / (n - 1)]
Empirical Rule percentages for normal distribution

Theorems

Empirical Rule (68-95-99.7 Rule)
Normal Distribution Theorem

Suitable Grade Level

Grades 10-12