Question

In a semiconductor manufacturing process, 3 wafers from a lot are tested. Each wafer is classified as pass or fail (binomial). Assume that the probability that a wafer passes the test is 0.7 and that the wafers are independent.

a. Fill in the table. Round answers to three decimal places (i.e. 0.123)

X Wafers Pass	P(X)	X*P(X)	(x-mu)2*P(X)
0	0.027	0	________Answer
1	_______Answer	_________ Answer	0.229
2	0.441	0.882	0.004
3	______Answer	1.029	0.278

b. What is the mean? Round answer to one decimal place (i.e. 1.2) Answer

c. What is the standard deviation? Round answer to three decimal places (i.e. 0.123)Answer

d. What is the probability of X > 1? Round answer to three decimal places

Answer 1

it is a binomial probability distribution,               because there is fixed number of trials,
               only two outcomes are there, success and failure
               trails are independent of each other
and probability is given by              

P(X=x) = C(n,x)*px*(1-p)(n-x)

where  
Sample size , n =    3
Probability of an event of interest, p =   0.7

a)

X	P(X)	X*P(X)			(X-mean)² * P(X)
0	0.027	0.000			0.119
1	0.189	0.189			0.229
2	0.441	0.882			0.004
3	0.343	1.029			0.278

b)

mean = E[X] = Σx*P(X) =            2.1

c)

variance=Σ(X-mean)² * P(X) = 0.63

std dev = √variance = √0.63 = 0.794

d)

P(X>1) = P(X=2) + P(X=3) = 0.189+0.343 = 0.784