Question

a chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. here are the data she has been given by each plant: plant volume of pollutant allegheny 0.44 l oglata 38.5 l macon 0.460 l what average volume should the chemical engineer report? be sure your answer has the correct number of significant digits.

Explanation:

Step1: Recall average formula

The formula for the average (arithmetic - mean) of a set of numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{x_1 + x_2+\cdots+x_n}{n}\). Here \(n = 3\), \(x_1=0.44\), \(x_2 = 38.5\), \(x_3=0.460\).

Step2: Calculate the sum of the volumes

\(S=0.44 + 38.5+0.460=39.4\)

Step3: Calculate the average

\(\bar{x}=\frac{S}{n}=\frac{39.4}{3}\approx13.1333\cdots\)
Since the least number of significant digits in the data is 3 (0.44 has 2 significant digits, 38.5 has 3 significant digits, 0.460 has 3 significant digits), we round the answer to 3 significant digits.

Answer:

\(13.1\) L