A graduate picks 25 exams at random from a total of 194 exams.Those 25 exams have a mean of 78.2% ± 17.1% (mean ± 1 standarddeviation). You may assume that these 25 exam scores areapproximately normally distributed.
a) Estimate the population mean exam score and its confidenceinterval for the 95% confidence level.
b) Estimate the population exam score standard deviation and itsconfidence interval for the 95% confidence level.
c) Estimate how many students failed the exam if the passinggrade is 60%.
d) Estimate how many students scored above 90% on the exam.
e) The graduate draws another set of exams of 25 exams, andthese exam scores are not normally distributed: they are skewedtowards a high score. What would you tell the graduate so that s/hecan estimate the population mean using methods we learned inclass?
