Question

Five hundred students in your school took the SAT test. Assuming that a normal curve existed for your school, how many of those students scored within 2 standard deviations of the mean? (Give the percent and the number.)

Answer 1

In order to find the percentage of students within 2 standard deviations, let's look at the z-table for the percentages when z = -2 and z = 2.

From the z-table, we have that the percentage for z = -2 is 0.0228 and for z = 2 is 0.9772.

The percentage between z = -2 and z = 2 is given by:

$0.9772-0.0228=0.9544$

Therefore the percentage is 95.44%.

Now, calculating the number of students within this percentage, we have:

$500\cdot0.9544=477.2$

Rounding to the nearest whole, we have 477 students.