It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

First let us define the variables in this problem:

variance, s^2 = 1.44         --->taking the square root gives                standard deviation, s = 1.2

margin of error, MOE = 0.25

confidence level = 0.99

N = number of students required

Using the standard distribution table for z, p = 0.99 occurs when z = 2.58

The formula for Margin of Error is given as:

MOE = z * s / sqrt N

0.25 = 2.58 * 1.2 / sqrt N

sqrt N = 12.384

N = 153.36 = 154

Therefore the sample should be at least 154 students to estimate the mean gpa within 0.25.