Question

The weights of Twinkies are Normally distributed with a mean of 1.5 ounces and a standard deviation of 0.1 ounces. a) The middle 99.7% of Twinkies weigh between approximately __________ and __________ ounces.

Answer 1

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.

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 = 1.5

Standard deviation = 0.1

middle 99.7%

Within 3 standard deviations of the mean, so

1.5 - 3*0.1 = 1.2

1.5 + 3*0.1 = 1.8

So the answer is:

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.