A company sells 10,000 motherboards annually. Each motherboard has a probability

Question

A company sells 10,000 motherboards annually. Each motherboard has a probability of 0.1 of failing
within the 1st year of operation. Each failed motherboard is returned and the company must provide
a new motherboard to the customer.

a. What is the probability that exactly 1000 of the original 10000 motherboards will be
returned?
b. What is the probability that 1000 or more of the original 10000 motherboards will be
returned?
c. What is the probability that 1100 or more of the original 10000 motherboards will be
returned?
d. What is the probability that 900 or fewer of the original 10000 motherboards will be
returned?

Explanation / Answer

here for normal approximation of binomial distribution

mean =np=10000*0.1 =1000

and std deviation =(np(1-p))1/2 =30

a) P(X=1000) =P(999.5<Z<1000.5)=P((999.5-1000)/30<Z<(1000.5-1000)/30)=P(-0.0167<z<0.0167)=0.5066-0.4934

=0.0133

b)P(X>=1000)=1-P(X<999.5)=1-P(Z<-0.0167)=1-0.4934=0.5066

c)P(X>=1100)=1-P(X<1099.5)=1-P(Z<3.3167)=1-0.9995=0.0005

d)P(X<=900)=P(X<900.5)=P(Z<-3.3167)=0.0005

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