Question

In a data set with mean of 12 and standard deviation of 4, at least what percent of data falls between 4 and 20?

Answer 1

Answer:

At least 95% of data falls between 4 and 20.

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 = 12

Standard deviation = 4

At least what percent of data falls between 4 and 20?

4 = 12 - 2*4

So 4 is two standard deviations below the mean

20 = 12 + 2*4

So 20 is two standard deviations above the mean

By the Empirical Rule, at least 95% of data falls between 4 and 20.