please make sure your answer is correct, thanks! The flow rate y (m^3/min) in a

Question

please make sure your answer is correct, thanks!

The flow rate y (m^3/min) in a device used for air-quality measurement depends on the pressure drop x (in. of water) across the devices filter. Suppose that for x values between 5 and 20:the two variables are related according to the simple linear regression model with true regression line y = -0.14 + 0.095x. (a) What is the expected change in flow rate associated with a 1 in. increase in pressure drop? Explain We expect the change in flow rate (x) to be the slope of the regression line. We expect the change in flow rate (y) to be the y-intercept of the regression line. We expect the change in flow rate (x) to be the y-intercept of the regression line. We expect the change in flow rate (y) to be the slope of the regression line. (b) What change in flow rate can be expected when pressure drop decreases by 5 in.? (c) What is the expected flow rate for a pressure drop of 10 in.? A drop of 18 in.? (d) Suppose sigma = 0.025 and consider a pressure drop of 10 in. What is th

Explanation / Answer

d) = 0.025, x=10 in -> y = 0.81 has distribution N(0.81, 0.0252)
P(y > 0.835) = P(z > (0.835 - 0.81)/0.025) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587

P(y > 0.840) = P(z > (0.840 - 0.81)/0.025) = P(z > 1.2) = 1 - P(z < 1.2) = 1 - 0.8849 = 0.1151

e) when x = 10 in, y = 0.81; when x = 11, y = 0.905;

Difference of the 2 distribution has distribution N(0.905 - 0.81, 0.0252 + 0.0252) = N(0.095, 0.03535532). Lets call the random variable X.

P(X < 0) = P(Z < (0-0.095)/0.0353553) = P(Z < -2.687) = 0.0036

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