Using four decimal digit accuracy, explain if the respective distribution applie

Question

Using four decimal digit accuracy, explain if the respective distribution applies and, if so, determine the probability that at least 5 and at most 7 of 1000 randomly tested micro circuits from a shipment of 25,000 will fail assuming that historically and consistently on average 1 in every 125 tested fails. If it applies, use a Binominal distribution If it applies, use a Poisson distribution If it applies, use a Normal distribution Briefly explain why statistically the preceding three results differ if they apply and differ

Explanation / Answer

This accounts for normal approximation to binomial, as n is large (n=1000) and p (1/125=0.008) is too small.

E(X)=np=1000*0.008=8, s=sqrt npq=sqrt 1000*0.008*0.992=2.8171

P(X>=5)=P[Z>=(5-8)/2.817]=P(Z>=-1.06)=0.8554

P(X<=7)=P[Z<=(7-8)/2.817]=P(Z<=-0.35)=0.3632

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