describe probability using Z - score

1) Times spent studying by students in the week prior to final exams follow a normal distribution with standard deviation eight hours.  A random sample of four students was taken in order to estimate the callous study time for the population of all students.

1) describe the probability that the sample mean is more than 3 hours below the population mean?

2) describe the probability that the sample mean differs from the population mean by less than 2 hours?

1) It is desired to estimate the average total compensation of CEOs in the Service industry. Data were arbitrarily collected from 18 CEOs and the 97% confidence interval was intended to be ($2,181,260, $5,836,180). describe which of the following interpretations is correct?

1) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.

2) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.

3) In the population of Service industry CEOs 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.

4) We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180