Question

The summer income of the 3,408 students at Van Buren High School last year was normally distributed with a mean of $1,751 and a standard deviation of $421. Approximately how many students had incomes less than $800? Round to the nearest integer.

a) 325 students
b) 444 students
c) 269 students
d) 587 students

Answer 1

Approximately 325 students had incomes less than $800.

Step-by-step explanation:

To find the number of students who had an income less than $800, we need to calculate the z-score for $800 and then use the standard normal distribution table.

The z-score is calculated as (x - mean) / standard deviation. In this case, the z-score is (800 - 1751) / 421 = -2.297.

Using the standard normal distribution table, we find that the area to the left of -2.297 is approximately 0.0113.

Multiplying this by the total number of students gives us approximately 0.113, which we can round to 11%.

Therefore, approximately 11% of the 3,408 students had incomes less than $800, which rounds to about 325 students.

Therefore, the answer is option a) 325 students.