Using the daily high and low temperature readings at Chicago’s O’Hare International Airport for an entire year, a meteorologist made a scatterplot relating y = high temperature to x = low temperature, both in degrees Fahrenheit. After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be μ_y = 16.6 + 1.02x with σ = 6.64°F.

a. According to the population regression line, what is the average high temperature on days when the low temperature is 40°F?

b. About what percent of days with a low temperature of 40°F have a high temperature greater than 70°F?

c. If the meteorologist used a random sample of 10 days to calculate the regression line instead of using all the days in the year, would the slope of the sample regression line be exactly 1.02? Explain your answer.