An exercise in Chapter 7 referred to a program designed to improve scores on the Graduate Record Examination (GRE). The class had 25 students and they scored a mean of 1075.00 on the GRE. Assuming the population standard deviation for the GRE \((\sigma)\) is 200 , estimate the mean GRE score for the population of students who take this program by calculating the \(95 \%\) confidence interval for the mean.

a. State the desired level of confidence.

b. Calculate the confidence interval and confidence limits.

(1) Calculate the population standard error of the mean \(\left(\sigma_{\bar{X}}\right)\).

(2) Identify the critical value of \(z\).

(3) Calculate the confidence interval and confidence limits.

c. Draw a conclusion about the confidence interval.