Question

Suppose a random sample of biweekly snowfalls in the pacific northwest has a sample mean of x¯=22.2 inches, with a sample standard deviation of s=3.5 inches. Since snowfall amounts in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule.

Between what two amounts are approximate 99.7% of the data?

Answer 1

Using the Empirical Rule, it is found that 99.7% of the data will be between 11.7 and 32.7 inches.

What does the Empirical Rule state?

It 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.

In this problem, considering the mean and the standard deviation of the data-set, the bounds between which 99.7% of the data-set are given by:

• 22.2 - 3 x 3.5 = 11.7 inches.

• 22.2 + 3 x 3.5 = 32.7 inches.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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