To lower manufacturing costs at an engineering company, they are trying to desig

Question

To lower manufacturing costs at an engineering company, they are trying to design printed circuit boards (PCBs) that can be reused on a number of products. For some products, not all components will be assembled on the board. For some products, all components will be assembled. After some study, a first PCB comes out and it has 8 sockets for a common chip. So up to 8 of these chips can be assembled. For the lower model of the product this will have 5 chips assembled and for the upper model, all 8 sockets will be populated. a) How many different ways can they assemble the 5 chips on the 8 empty sockets? b) Suppose they start production of a medical version of the same product. The medical model is based on the upper model, where all 8 sockets are filled. But now, on 4 of the sockets high-grade, high-quality chips are assembled, and on the remaining 4 low-grade commercial chips are assembled. How many different ways can they assemble the 8 chips now? A random sample of n1 = 16 is selected from a population with a mean of 75 and standard deviation of 8. A second random sample of n2 = 9 is selected from a different population with a mean of 70 and standard deviation of 12. Let XM1 and XM2 denote the means of the samples respectively. a) Find the probability that XM1-XM2 > 4 b) Find the probability that 3, 5

Explanation / Answer

here mean of A= XM1 -XM2 =5

and std deviation=(82/16+122/9)1/2 =4.472

a) hence P(A>4) =1-P(A<4)=1-P(Z<(4-5)/4.472)=1-P(Z<-0.2236)=1-0.4115=0.5885

b)P(3.5<X<4.5)=P(-0.3354<Z<-0.1118)=0.4555-0.3687 =0.0868

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