Researchers for a manufacturer of barometers (devices to measure atmospheric pressure) read each of 50 barometers at the same time of day. The mean of the readings is 30.4 (inches of mercury) with a standard deviation of 0.23 inch, and the readings appear to be normally distributed.

a. What percentage of the barometers read over 31?

b. What percentage of the barometers read less than 30?

c. The company decides to reject barometers that read more than 1.5 standard deviations above or below the mean. What is the critical reading below which barometers will be rejected? What is the critical reading above which barometers will be rejected?

d. What would you take as the actual atmospheric pressure at the time the barometers were read? Explain.