Question

A university has 31,560 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of students at the university who speak three or more languages.

The expected number of students at the university who speak three or more languages is?

Answer 1

Hello there!

Here's the information given to us written out:

- 31560 total students

- 12/180 students speak 3 or more

To solve:

To solve this, use the probability from the survey of 180 students to make a reasonable estimate for the 31560 total students.

12/180 students were able to speak 3 or more languages. This proportion, of 12 students : 180 students can be adjusted.

Just like when simplifying fractions, both sides can have an operation (of multiplication or division) done to it and still be equivalent.

In this case, we want to set the side of total students to be equivalent to 31560 to get the estimated number of students that speak 3 or more languages.

To get the number to multiply both sides by:

31560 / 180 = 175 1/3 = 526/3

Now, carry out the operation - multiply both sides by that number.

12/180 = (12 * 526/3) / (180 * 526/3) = 2104 / 31560

So, out of 31560, using the same probability, around 2104 students would speak 3 or more languages.

Hope this helped!