Question

An airline shopping company takes orders through its website every day of the week. The company maintains that 80% of orders from the website are shipped within 24 hours. The quality controller selects 10 orders at random to check when they are shipped. Find the probability that

a. Exactly 8 of these are shipped within 24 hours,

b. At least 8 of these orders are shipped within 24 hours.

c. On average, the company found that 5 orders are usually returned for a refund every day. Find the probability that on one particular day exactly 3 orders are returned for a refund.

Answer 1

here this is binomial with parameter n=10 and p=0.8

a)

P(  Exactly 8 of these are shipped within 24 hours)

probability =

P(X=8)=

(10C8)0.82(1−0.8)(10-8)    =

0.3020

b)

P(At least 8 of these orders are shipped within 24 hours)

probability =

P(X>=8)=

P(X=8)+P(X=9)+P(X=10)=

(10C8)0.82(1−0.8)(10-8)+(10C9)0.89(1−0.8)(10-9)+(10C8)0.810(1−0.8)(10-10)=

0.6778

c)

probability that on one particular day exactly 3 orders are returned for a refund =P(X=3)=e^-55³/3! =0.1404