Using the health records of every student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x=age (in years). After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be μ_y = 105 + 4.2x with σ = 7 cm.

a. According to the population regression line, what is the average height of 15-year-old students at this high school?

b. About what percent of 15-year-old students at this school are taller than 180 cm?

c. If the nurse used a random sample of 50 students from the school to calculate the regression line instead of using all the students, would the slope of the sample regression line be exactly 4.2? Explain your answer.