Question

Eighty percent of students in your school own a bike. Of a sample of students in your school, the ratio of students who own a bike to students who do not own a bike is 8 : 2. Does the sample closely estimate the percentage of students in your school who own a bike?

Answer 1

Answer:

Yes, the sample closely estimates the percentage of students in the school.

Step-by-step explanation:

Given that:

Percentage of students in school who own a bike = 80%

Ratio of students who own a bike to students who do not own a bike = 8 : 2

To find:

Whether the sample closely estimates the percentage of students who own a bike ?

Solution:

First of all, let us convert the ratio in percentage form.

Percentage formula is given as follows:

$\dfrac{Favorable\ cases}{Total\ Number\ of\ cases}\times 100$

Here,the ratio given is 8:2.

Let number of students who ride bike = $8x$

Let number of students who do not ride bike = $2x$

Total number of students = $10x$

So, the percentage of students who ride a bike:

$\dfrac{8x}{10x}\times 100 = \bold{80\%}$

So, the sample percentage is equal to the percentage of students in school who own a bike.

Therefore, the sample closely estimates the percentage of students who own a bike.