Question

A large industrial firm allows a discount on any invoicethatispaidwithin30days.Ofallinvoices,10% receive the discount. In a company audit, 12 invoices are sampled at random.

a. What is the probability that exactly four of them receive the discount?

b. What is the probability that fewer than three of them receive the discount?

c. What is the probability that none of them receive the discount?

d. Find the mean number that receive the discount.

e. Find the standard deviation of the number that receive the discount.

Answer 1

here this is binomial distribution with parameter n=12 and p=0.10

a)

probability =

P(X=4)=

(nCx)px(1−p)(n-x)    =

0.0213

b)

probability that fewer than three of them receive the discount :

probability =

P(X<=2)=

∑x=0x     (nCx)px(1−p)(n-x)    =

0.8891

c)

probability that none of them receive the discount :

probability =

P(X=0)=

(nCx)px(1−p)(n-x)    =

0.2824

d)

here mean of distribution=μ=np=

1.20

e)

standard deviation σ=√(np(1-p))=

1.0392