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.
