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

cistG 2020-12-28 Answered

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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Expert Answer

Viktor Wiley
Answered 2020-12-29 Author has 84 answers

Step 1
Given:
[μy=16.6+1.02xri>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=xμσ=7057.46.641.90]
Determine the corresponding probability using the normal probability table in the appendix. [P(Z<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>70)=P(Z>1.90)
=1P(Z<1.90)
=10.9713
=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%

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