7.83 Students’ scores on the final statistics test from the previous semester at a university were taken for a random sample of 9 students and were recorded as follows:

69 92 82 30 73 91 48 74 62

a. Find the most efficient estimates of the population mean and variance.

b. Estimate the proportion of the students’ statistics final exam scores greater than 75%.

7.84 The organizers of an economic conference selected a random sample of 180 participants to determine the actual duration of each person’s presentation. The sample mean duration was 18.52 minutes with a standard deviation of 5.25 minutes. Based on these results, a confidence interval between 18.42 and 18.62 minutes was calculated for the population mean. Find the probability content for this interval.