Question

Of the 200 envelopes carried by a mail track, 120 are from city K and the rest are from city J. Forty

percent of the envelopes from city K are birthday cards, and thirty percent of the envelopes from city J

are birthday cards. A random sample of 20 envelopes is randomly selected from the mail track. Find

the variance of the number of birthday cards among a 20 randomly selected envelopes from this mail

track.

Answer 1

Ans:

P(city K)=120/200=0.6

P(city J)=80/200=0.4

P(birthday card/city K)=0.40

P(birthday card/city J)=0.30

P(birthday cards)=0.40*0.6+0.30*0.4=0.36

Now use binomial distribution with n=20 and p=0.36

Variance of the number of birthday cards=np(1-p)=20*0.36*(1-0.36)=4.608