Wafers of type A have thickness with a mean of 134.9 and standard deviation of 0

Question

Wafers of type A have thickness with a mean of 134.9 and standard deviation of 0.7, while wafers of type B have thickness with a mean of 138.2 and a standard deviation of 1.1. The thickness of the wafers are all independent of each other.

a) Three wafers of type A are stacked on top of each other. What are the mean and the standard deviation of the total thickness?
b) Two wafers of type A and two wafers of type B are stacked on top of each other. What are the mean and the standard deviation of the total thickness?
c) Four wafers of type A and three wafers of type B are taken. What are the mean and the standard deviation of the average thickness of these seven wafers?

Explanation / Answer

Wafers of type A have thickness with a mean of 134.9 and standard deviation of 0.7, while wafers of type B have thickness with a mean of 138.2 and a standard deviation of 1.1. The thickness of the wafers are all independent of each other.

mean =3*134.9 =404.7

standard deviation of the total thickness =sqrt( 0.72+0.72+0.72)=1.2124

mean =2*134.9 +138.2 =408

standard deviation of the total thickness =sqrt( 0.72+0.72+1.12)=1.4799

c) Four wafers of type A and three wafers of type B are taken. What are the mean and the standard deviation of the average thickness of these seven wafers?

mean =4*134.9 +3*138.2 =954.2

standard deviation of the total thickness =sqrt( 4*0.72+3*1.12)=2.3643

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