Probability using the Z - score.

1. Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of four students was taken in order to estimate the mean study time for the population of all students.

a. What is the probability that the sample mean is more than three hours below the population mean?

b. What is the probability that the sample mean differs from the population mean by less than 2 hours?

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

1.97 percent of the sampled total compensation values fell between $2,181,260 and $5,836,180.

2. We are 97 percent 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 percent of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.

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