Question

1. (4.64/7 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 12.E.011.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 4.10 - 0.01x and c = 0.07. USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase -0.01 hr 9°F increase -0.09 hr (b) What is the expected reaction time when temperature is 210°F? When temperature is 260°F? 210°F 2 hr 260°F 1.5 hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 1.39 and 1.61 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.)

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Answer 1

Anso 1)) Given pegression model is y= 4.10 -0.0106 Also, 6=0.07. Hence, awe laye, 4(2) = o 4,10 -0.01% po feen, 4 (260) - 4.10 -0.01 X260 = 1.5. P (1.39 <Y< 1.61) - P ( 1139-15, Y-42601-61-1.5 1.6 - 15 =P(-1.57€ z { 1.57) 0.07 o = 0.8836 for timer observation. P (1.39 27; <1.61) 2.0.8836 for, i = 1, 2, 3, 4, 5 p(9.8937131.60), ..., 149SY<1-6)) = XT, P (1995> <1«61) (0.8836) 0.5386 The probability that all five times are between ling and 1.61 hours 15 0.5386 Then E-0.01 Let, Y and Y2 be the two independent reaction time, BOY:-72) = f(Y,) - (87) = 4.10 - 0.01 (2+i) -(4-10-2013) Var (Y, 72) Var(r)+ var(72) = 204 SD (Y; V2) - Iver (Y=12] = 262 2828= V2X0,07 Faces 299899. P(x)) = P(Y-13.90)=P(*-* -64 te, sono *P(2> 0.101) "The peavined probability is 10.4602 0.09899 SD(%1-82) 20.4602