Suppose that in a certain chemical process the reaction tine y?hr) is related to

Question

Suppose that in a certain chemical process the reaction tine y?hr) is related to the temperature ("F) in the chanter i, which the reaction takes place according to the simple-regression mo del Hith equi y-4.50-0.01x and?-0.08. (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 12F increase in temperature? 1"F Increase 01 12 F increase 0 12 (b) what is the expected reaction time when temperature is 200 F? When temperature is 240 F7 200 F 25 240F2 e) Suppose five obervations are made independently on reaction time, each one for a temperature of what t he probability that all live times are between 1.98 and 2.22 hours? (Round your (d) What is the probability that two independently ( oserved 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 )

Explanation / Answer

c)

probability that one observation is between 1.98 and 2.22 =P(1.98<X<2.22)

=P((1.98-2.1)/0.08<Z<(2.22-2.1)/0.08)=P(-1.5<Z<1.5)=0.9332-0.0668=0.8664

hence probability that all 5 times between 1.98 and 2.22 =(0.8664)5 =0.4882

d)

here mean difference between 1 degree apart temperature =-0.01

std deviation =(0.082+0.082)1/2 =0.113

hence Probability =P(X>0)=P(Z>(0-(-0.01)/0.113)=P(Z>0.09)=0.4641

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