Weights measured in grams of randomly selected M&M plain candies: 0.957 0.912 0.925 0.886 0.920 0.958 0.915 0.914 0.947 0.939 0.842

What is the range of weights of the middle 99.7% of M&M’s?

(round to the ten thousandths place)

The range of weights of the middle 99.7% of M&M’s is between 0.8187 and 1.0203.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Sample mean:

Sample standard deviation:

What is the range of weights of the middle 99.7% of M&M’s?

By the Empirical Rule, within 3 standard deviations of the mean, so:

0.9195 - 3*0.0336 = 0.8187.

0.9195 + 3*0.0336 = 1.0203.

The range of weights of the middle 99.7% of M&M’s is between 0.8187 and 1.0203.

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