Answer to Question #105293 in Statistics and Probability for Simon mwanthi

Question

For the past records about40% of a firm orders are for export. Their record for export is 48% in one particular financial quarter. If they expect to satisfy about 80 orders in the next financial quarter, what is the probability that they will break their previous export record

Answer 1

Normal approximation of the binomial distribution with

$\mu=np=80*0.48=38.4,\;\;\sigma=\sqrt{np(1-p)}=\sqrt{80*0.48(1-0.48)}\approx4.47$

can be used.

So, the probability that they will break their previous export record $80*0.4=32$ orders is

$P(X>32)=P(Z>\frac{32-38.4}{4.47})=P(Z>-1.43)=0.9236.$