Data presented in the article “Manganese Intake and Serum Manganese Concentration of Human Milk-Fed and Formula-Fed Infants” (American Journal of Clinical Nutrition [1984]: 872–878) suggest that a simple linear regression model is reasonable for describing the relationship between y = serum manganese (Mn) and x = Mn intake (mg/kg/day). Suppose that the true regression line is y = −2 + 1.4x and that σ = 1.2. Then for a fixed x value, y has a normal distribution with mean −2 + 1.4x and standard deviation 1.2.

a. What is the mean value of serum Mn when Mn intake is 4.0? When Mn intake is 4.5?

b. What is the probability that an infant whose Mn intake is 4.0 will have serum Mn greater than 5?

c. Approximately what proportion of infants whose Mn intake is 5 will have a serum Mn greater than 5? Less than 3.8?