The Intake valve clearances on new engines of a certain typeare normally distrib

Question

The Intake valve clearances on new engines of a certain typeare normally distributed with mean 200um and standard deviation10um. a) What is the probability that the clearance is greater than215 um? b) What is the probability that the clearance is between 180and 205um? c) Suppose that a lot of 20 valves are randomly selected. Whatis the probability that their average clearange is greater than205um? d) What would an engine's intake valve clearance need to be inorder for it to be among the top 25% of highest clearancevalues? The Intake valve clearances on new engines of a certain typeare normally distributed with mean 200um and standard deviation10um. a) What is the probability that the clearance is greater than215 um? b) What is the probability that the clearance is between 180and 205um? c) Suppose that a lot of 20 valves are randomly selected. Whatis the probability that their average clearange is greater than205um? d) What would an engine's intake valve clearance need to be inorder for it to be among the top 25% of highest clearancevalues?

Explanation / Answer

a) What is the probability that the clearance is greater than215 um?
P(X>215)=P((x-)/ >(215-200)/10) = P(Z> 1.5) = 0.0668 (check normaltable)

b) What is the probability that the clearance is between 180and 205um?
P(180<X<205) = P((180-200)/10 < Z <(205-200)/10) = P(-2<Z<0.5) = 0.6687 (check normaltable)

c) Suppose that a lot of 20 valves are randomly selected. Whatis the probability that their average clearange is greater than205um?
P(xbar>205)=P((xbar-)/(/n)> (205-200)/(10/sqrt(20))) = P(Z> 2.24) = 0.0125 (checknormal table)

d) What would an engine's intake valve clearance need to be inorder for it to be among the top 25% of highest clearancevalues?

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