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Medicine and Clinical Studies Officials at the U.S. Environmental Protection Agency worked with…

Medicine and Clinical Studies Officials at the U.S. Environmental Protection Agency worked with hospital physicians in Anaheim, California, to examine the relationship between environmental pollution and illness. A random sample of summer days was selected, and at 2:00 p.m. on each day the air quality was assessed by measuring the concentration of carbon monoxide (x, in ppm). Illness was measured by counting the number of new patients (y) seen for respiratory problems at the hospital that day. Suppose the true regression line is y = 25.1 + 0.9x.

a. Find the expected number of respiratory patients at the hospital on a day when the carbon monoxide concentration is 12 ppm.

b. What is the expected change in the number of patients per day if the carbon monoxide concentration decreases by 5 ppm?

c. Suppose σ = 1.2. Find the probability that an observed number of patients is between 5 and 7 when the carbon monoxide concentration is 13 ppm.