You want to do a study of where students sit and their GPA

Given Information

Standard deviation of students GPA (σ)(σ): 1.25

Confidence level: 90%

Width of confidence interval (Margin of Error E): 0.25

The critical value at 90% confidence interval for proportions is ??Zα2??(Zα2)

where \alpha is the level of significance and is calculated as,

α=1−0.90=0.1α=1−0.90=0.1

Using the significance level, the critical value is obtained using the Z-table as follows,

Zα2=Z0.05=1.645Zα2=Z0.05=1.645

The minimum number of students (sample size) is calculated as,

MinimumSamplesize=(z⋅σE)2=(1.645×1.250.25)2=67.65≈68MinimumSamplesize=(z⋅σE)2=(1.645×1.250.25)2=67.65≈68

Thus, the minimum number of students should survey is 68.