Question

There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.

a. 804
b. 844
c. 884
d. 0.36

Answer 1

A. 804

Explanation:

Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.

Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229

Also, the ratio of the sample students with math score below grade level to sample population will be 163:452

On equating both ratios, we will have;

x:2229 = 163:452

`(x)/(2229) = (163)/(452)\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = (2229*163)/(452)\\ \\x = (363,327)/(452)\\ \\x = 803.8\\\\x \approx 804`

Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804