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Suppose that a random sample of adult males has a sample mean heart mass of x¯=310.1 grams, with a sample standard deviation of s=6.6 grams. Since adult male heart masses are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two masses do approximately 68% of the data occur? Round your answer to the nearest tenth.

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Answer:

Between 303.5 grams and 316.7 grams

Step-by-step explanation:

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

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

95% of the measures are within 2 standard deviation of the mean.

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

In this problem, we have that:

Mean = 310.1 grams

Standard deviation = 6.6 grams

Between what two masses do approximately 68% of the data occur?

By the Empirical Rule, within 1 standard deviation of the mean.

310.1 - 6.6 = 303.5 grams

310.1 + 6.6 = 316.7 grams

Between 303.5 grams and 316.7 grams

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