Question

After a million measurements of thing x, we find a sample mean of 30.49 and standard deviation of 1.95. What chance, in percent (0-100) does the next measurement have of being outside 1 standard deviation from the mean?

Answer 1

32%

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.

The sampling distribution of the sample means tend to be normally distributed.

What chance, in percent (0-100) does the next measurement have of being outside 1 standard deviation from the mean?

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

100 - 68 = 32% are outside of 1 standard deviation from the mean.

So the chance is 32%.