Question

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 = 5.20 − 0.01x and σ = 0.065.

(a) What is the expected change in reaction time for a 1°F increase in temperature? For an 8°F increase in temperature?

1°F increase		hr
8°F increase		hr

(b) What is the expected reaction time when temperature is 210°F? When temperature is 260°F?

210°F		hr
260°F		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 2.45 and 2.75 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.)

Answer 1

a)expected change in reaction time for a 1°F increase in temperature =-0.01

expected change in reaction time for a 8°F increase in temperature =-0.08

b)

expected reaction time when temperature is 210°F =5.20-0.01*210=3.1

expected reaction time when temperature is 260°F =5.20-0.01*210=2.6

c)for 1 time

P(2.45<X<2.75)=P(-0.15/0.065<Z<0.15/0.065)=P(-2.31<Z<2.31)=0.9792

hence for 5 times; probability that all five times are between 2.45 and 2.75 hours =0.9792⁵ =0.9002

d)

P(X>0)=P(Z>(0.01/(0.065*sqrt(2))=P(Z>0.11)=0.4562