Problem 4 A chip manufacturer makes defective chips with pro

Problem 4. A chip manufacturer makes defective chips with probability 0.1 and non-defective chips with probability 0.9. Assume that chips are independent - i.e. whether one chip is defective is independent of whether another chip is defective or not. Let D be a random variable corresponding to the number of defective chips in a batch of n chips. 1. What is E[D1000], the expected number of defective chips in a batch of 1000 chips? 2. What is the standard deviation of the number of defective chips in a batch of 1000 chips?

Solution

(3)mean=n*p=1000*0.1=100

standard deviation =sqrt(n*p*(1-p))

=sqrt(1000*0.1*0.9)

=9.486833

So the probability is

P(X>50) = P((X-mean)/s >(50-100)/9.486833)

=P(Z>-5.27) = 0.9999 (from standard normal table)

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(4) P(50<X<150)

=P((50-100)/9.486833<Z<(150-100)/9.486833)

=P(-5.27<Z<5.27)

=0.9999 (from standard normal table)