A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that the student population studied an average of 20 hours per week with a standard deviation of 10 hours.
(a) What is the standard error of the mean?
(b) What is the probability that a sample mean would exceed 20 hours per week?
(c) What is the probability of finding a sample mean less than 18 hours?
(d) What is the probability that average student study time is between 18 and 22 hours?