Question

Question 7 An electronic product contains 44 integrated circuits. The probability that any integrated circuit is defective is 0.02, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates? Round your answer to four decimal places (e.g. 98.7654). The probability is

Answer 1

here this is binomial with parameter n=20 and p=0.677

a)

P(X>=1)=1-P(X<=0)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

1.0000

b)

P(X>=5)=1-P(X<=4)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

1.0000

c)

mean E(x)=μ=np=20*0.677 =13.54

d)

standard deviation σ=√(np(1-p))=2.09