1. For the population of females between the ages of 3 and 74 who participated in the National Health Interview Survey, the hemoglobin level is approximately normally distributed with mean 13.3g/100ml and standard deviation 1.12g/100ml.
(a) If a sample of size 15 is selected from this population, what is the probability that the mean hemoglobin level of the sample is between 13.0g/100ml and 13.6g/100ml?
(b) If a sample of size 30 is selected from this population, what is the probability that the mean hemoglobin level of the sample is between 13.0g/100ml and 13.6g/100ml?
2. Suppose that college faculty with the rank of professor at two-year institutions earn an average of $64,571 per year with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all two-year institutions in the United States and the average salary was calculated.
(a) Describe the sampling distribution of the sample mean
(b) Within what limits would you expect the sample average to lie, with probability 0.95?
(c) Calculate the probability that the sample mean is greater than $66,000?
(d) If your random sample actually produced a sample mean of $66,000, would you consider this unusual? What conclusion might you draw?