According to a survey, the average number of 9 ounce coffee cups consumed daily is 3.1 Assume that the standard deviation is 0.5 cup. A researcher surveys the daily coffee consumption habits in the state of Washington D.C. He draws a sample of 36. Calculate the probability that the sample mean will be

a. between 3 and 3.01?

b. greater than 3.2?

c. less than 3?

d. Calculate the range of the sample average mean for the middle 95% area within which the sample means will lie.

e. If the researcher is willing to limit the standard error to 1.5% of population mean, is the sample size large enough?

f. If the researcher is willing to limit the standard error to 3% of population mean, then what should be the sample size?