Aresearch study investigated differences between male and female students. based on the study results, we can assume the population mean and standard deviation for the gpa of male students are µ = 3.5 and σ = 0.5. suppose a random sample of 100 male students is selected and the gpa for each student is calculated. what is the probability that the random sample of 100 male students is selected and the gpa for each student is calculated. find the interval that contains 95.44 percent of the sample means for male students.

Arandom sample of 15 observations is used to estimate the population mean. the sample mean and the standard deviation are calculated as 172 and 63, respectively. assume that the population is normally distributed. a. with 99 confidence, what is the margin of error for the estimation of the population mean? b. construct the 99% confidence interval for the population mean. c. construct the 95% confidence interval for the population mean. d. construct the 83% confidence interval for the population mean. hint: you need to use excel function =t.inv.2t to find the value of t for the interval calculation.