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 [μy=16.6+1.02]with[σ=6.6+∘F]. About what percent of days with a low temperature of 40∘ F have a high temperature greater than 70∘ F?

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Using the daily high and low temperature readings at Chicago&#039;s O&#039;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 [μy=16.6+1.02]with[σ=6.6+∘F]. About what percent of days with a low temperature of 40∘ F have a high temperature greater than 70∘ F?

Viktor Wiley · Accepted Answer

Step 1 Given: [μy=16.6+1.02xri&amp;gt;h] (Equation population regression line) [σ=6.64] The average high temperature on days where the low temperature is 40∘ F according to the population regression line can be found by replacing 2 in the regression line equation by 40 and evaluating. [μy=16.6+1.02(40)=16.6+40.8=57.4] Thus the mean is 57.4 and the standard deviation is 6.64. Since the conditions are met, the response y varies according to a Normal distribution. The z-score is the value decreased by the mean, divided by the standard deviation. [z=x−μσ=70−57.46.64≈1.90] Determine the corresponding probability using the normal probability table in the appendix. [P(Z&amp;lt;1.90)] is given in the row starting with 1.9 and in the column starting with .00 of the standard normal probability table in the appendix. P(X&amp;gt;70)=P(Z&amp;gt;1.90) =1−P(Z&amp;lt;1.90) =1−0.9713 =0.0287 =2.87% Thus about 2.87% of the days with a low temperature of 40∘ F are expected to have a high temperature that is greater than 70∘ F. Result: 2.87%

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot rel

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