Suppose That in a Certain Chemical Process the Reaction Time $(\left.{ \degree}{\mathrm{F}}\right)$

Essay

Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature $(\left.{ \degree}{\mathrm{F}}\right)$
in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.00 - .01x and $\sigma$ = .075.
a. What is the expected change in reaction time for a $1 ^ { \circ }$
F increase in temperature? For a 10 ${ \circ }$
F increase in temperature?
b. What is the expected reaction time when temperature is 200 ${ \circ }$

F? When temperature is 250 ${ \circ }$

F?
c. Suppose five observations are made independently on reaction time, each one for a temperature of 250 ${ \circ }$

F. What is the probability that all five times are between 2.4 and 2.6 hours?
d. What is the probability that two independently observed reaction times for temperatures $1 ^ { \circ }$
apart are such that the time at the higher temperature exceeds the time at the lower temperature?