Question

If a variable has a distribution that is bell-shaped with mean 28 and standard deviation 5, then according to the Empirical Rule, 99.7 of the data will lie between which values?

According to the Empirical Rule, 99.7% of the data will lie between __and__

Answer 1

According to the Empirical Rule, 99.7% of the data will lie between the values 13 and 43.

Step-by-step explanation:

The Empirical Rule states that for a bell-shaped distribution with a mean of 28 and a standard deviation of 5, 99.7% of the data will lie between three standard deviations of the mean. To find these values, we can use the formula:

Lower bound = mean - (3 * standard deviation)

Upper bound = mean + (3 * standard deviation)

Substituting the given values, we get:

Lower bound = 28 - (3 * 5) = 28 - 15 = 13

Upper bound = 28 + (3 * 5) = 28 + 15 = 43

Therefore, according to the Empirical Rule, 99.7% of the data will lie between the values 13 and 43.