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=((100*2)+(90*8)+(85*6)+(78*2)+(65*3))/(21)`
`Mean=(200+720+510+156+195)/(21)=(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)=(3)/(21)=(1)/(7)\text{ \lparen or}\approx14.3\text{\%\rparen}`

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