Question

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 14.1 pounds and 16.2 pounds, respectively.Calculate the expected value and the standard deviation of this distribution.

Answer 1

Answer:

Mean = 15.15

Standard deviation = 0.6062

Step-by-step explanation:

We are given a uniform distribution of  quantity to be put in each bag.

Low and high filling weights:

14.1 pounds and 16.2 pounds

a = 14.1

b = 16.2

a) Mean:

$\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{14.1+16.2}{2} = 15.15$

b) Standard Deviation:

$\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\dfrac{(16.2-14.1)^2}{12}} = \sqrt{0.3675} = 0.6062$