Question

the advertised weight on a can of soup is 10 ounces. the actual weight in the cans follows a uniform distribution and varies between 9.3 and 10.3 ounces. compute the standard deviation of the weight of a can of soup.

Answer 1

The standard deviation of a uniform distribution is calculated using the formula:

$$\sqrt{\frac{(b-a)^2}{12}}$$

where `a` is the minimum value and `b` is the maximum value. In this case, `a` is 9.3 ounces and `b` is 10.3 ounces. Substituting these values into the formula gives:

$$\sqrt{\frac{(10.3-9.3)^2}{12}} = \sqrt{\frac{1^2}{12}} = \sqrt{\frac{1}{12}} \approx 0.29 \text{ ounces}$$

So, the standard deviation of the weight of a can of soup is approximately 0.29 ounces.

Explanation: