Question

The following table shows the record of the weight of all boxes in an EMS delivery truck.

Weight of box (lb)	No. of boxes
1-10	8
11-20	7
21-40	5

a) If you randomly select 8 boxes from this truck without replacing the box after each pick, what is the probability that at least 6 of them are 10 pounds or lighter?

b) If you randomly select 8 boxes from this truck with replacing the box after each pick, what is the probability that at least 6 of them are 10 pounds or lighter?

Answer 1

here let X follows number of boxes which are 10 pounds or lighter

without replacement:

here this is hypergeometric distribution with parameter:
sample size n=	8
population N=	20
success size k=(number of total boxes 10 pound or lighter)=	8

a)

P(X>=6)=1-P(X<=5)=

1-∑x=05     (8Cx)(20-8C8-x)/(20C8) =

0.0154

b)

with replacement:

here this is binomial with parameter n=8 and p=8/20 =0.4

  probability that at least 6 of them are 10 pounds or lighter:

P(X>=6)=1-P(X<=5)=

1-∑x=05 (8Cx)0.4x(0.6)(8-x) =

0.0498