Suppose in a large class, students' grade in a test followed the normal distribution. Approximatley what percent of grades is between two standeard deviation below the mean and two standar deviation above the mean (that is in between Xbar-2S and Xbar+2S grades) ? note, Xbar is the mean and S is standard deviation.

Question

Lilliana Zavala

Mathematics

26 November, 14:08

Suppose in a large class, students' grade in a test followed the normal distribution. Approximatley what percent of grades is between two standeard deviation below the mean and two standar deviation above the mean (that is in between Xbar-2S and Xbar+2S grades) ? note, Xbar is the mean and S is standard deviation.

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Yuliana · Answer 1

95%

Step-by-step explanation:

Given that in a large class, students' grade in a test followed the normal distribution.

The normal distribution is symmetric about the mean, bell shaped and having area of more than 99% between 3 std deviations from the mean on either side.

We are to find the percent of grades is between two standeard deviation below the mean and two standar deviation above the mean (that is in between Xbar-2S and Xbar+2S grades)

where x bar is the mean and s = std devition

This is equivalent to 100*Prob that X lies between these two values

As per normal distribution curve 68, 95, 99 rule we get

approximately 95% lie between these two values.