Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Thirty randomly selected students took the calculus final. If the sample mean was 78 and the standard deviation was 7.5, construct a 99 percent confidence interval for the mean score of all students. Assume that the population has a normal distribution.
A) 75.67 < μ < 80.33
B) 74.23 < μ < 81.77
C) 74.24 < μ < 81.76
D) 74.63 < μ < 81.37