The breaking strength of a rivet has the average of 10,520 psi and the standard

Question

The breaking strength of a rivet has the average of 10,520 psi and the standard deviation of 480 psi. Answer the following questions.

a. A random sample of 55 rivets was selected. Find the probability that the average breaking strength of these rivets exceeds 10,640 psi. ANSWER: _______________________________________________

b. In case a random sample of 34 rivets was selected, find the probability that the average breaking strength of these rivets is between 10,356 and 10,765 psi. ANSWER: ________________________________________________

c. If a random sample of 26 rivets was selected, find the probability that the average breaking strength of these rivets is less than 9,248 psi. ANSWER: __________________________________________________________

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =480/(55)1/2 =64.723

probability that the average breaking strength of these rivets exceeds 10,640 psi =P(X>10640)

=1-P(X<10640) =1-P(Z<(10640-10520)/64.723)=1-P(Z<1.8540)=1-0.9681 =0.0319

b) std error of mean =std deviation/(n)1/2 =480/(34)1/2 =82.319

probability that the average breaking strength of these rivets is between 10,356 and 10,765 psi.

=P(10356<X<10765)=P(-1.9922<Z<2.9762)=0.9985-0.0232 =0.9754

c)

std error of mean =std deviation/(n)1/2 =480/(26)1/2 =94.136

probability that the average breaking strength of these rivets is less than 9,248 psi.=P(X<9248)

=P(Z<-13.5124)=0.0000

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