Question

75 students were surveyed about their homework habits. 21 of those students say they spend less than 10 minutes on homework each night. If there are 1,500 students in the school, predict the number of students who would say they spend less than 10 minutes in homework each night

Answer 1

Given:

Sample size = 75 students

Students who spend less than 10 minutes on homework each night = 21

Total students in the school = 1500

To find:

Estimated number of students who would say they spend less than 10 minutes in homework each night.

Solution:

Let A be the event that the student spends less than 10 minutes in homework each night.

Then, the probability that the student spends less than 10 minutes in homework each night is

`P(A)=\frac{\text{Students who spend less than 10 minutes on homework}}{\text{Sample size}}`

`P(A)=(21)/(75)`

`P(A)=(7)/(25)`

Now, total students in the school is 1500. So, multiply 1500 with P(A) to get the umber of students who would say they spend less than 10 minutes in homework each night.

`1500\cdot P(A)=1500* (7)/(25)`

`1500\cdot P(A)=420`

Therefore, estimated number of students who would say they spend less than 10 minutes in homework each night is 420.