Question

Use the data in the table shown to calculate the following.1. population mean for the semester grades2. population proportion of students who earned a grade less than 70

Answer 1

The Solution:

Given:

Required to find:

1. population mean

2. population proportion of students who earned a grade less than 70.

Step 1:

The population mean.

$Mean=\frac{(100\times2)+(90\times8)+(85\times6)+(78\times2)+(65\times3)}{21}$$Mean=\frac{200+720+510+156+195}{21}=\frac{1781}{21}=84.810\approx84.8$

Thus, the population mean is 84.8

Step 2:

$Proportion(student\leq70)=\frac{Number\text{ of students that earned less than 70}}{Total\text{ number of students}}$$Proportion(student\leq70)=\frac{3}{21}=\frac{1}{7}\text{ \lparen or}\approx14.3\text{\%\rparen}$

Therefore, the required proportion is 1/7 or 14.3%