Question

The number of blueberries in a blueberry muffin baked by EarthHarvest Bakeries can range from 20 to 40 blueberries. (a) Use the Empirical Rule to estimate the standard deviation of the number of blueberries in a muffin. (Round your answer to the nearest whole number.) Standard deviation (b) What assumption did you make about the distribution of the number of blueberries

Answer 1

a) Standard deviation: 3 bluberries

b) We assume, to apply this rule, that the distribution of blueberries per muffin has a bell-curve distribution, approximately normal.

Explanation:

We know that the number of blueberries in a blueberry muffin baked by EarthHarvest Bakeries can range from 20 to 40 blueberries.

a) If we use the Empirical Rule 68-95-99.7, specifically the last term, we have that:

- 99.7% of the data will fall between 3 standard deviations from the mean.

Then, if we consider the range of 20 to 40 containing 99.7%, we can calculate the standard deviation as:

`UL-LL=2*(3\sigma)\\\\40-20=6\sigma\\\\ \sigma=20/6=3.33\approx 3`