The US Postal Service claims that 85 of its next day Express

The U.S. Postal Service claims that 85% of its \"next day\" Express Mail actually reaches its intended recipient on the day after it is mailed.

(a) A company sends out 20 pieces of Express Mail to clients. If the Postal Services calim is true, what is the probability that all the mail will be delivered the next day?

(b) What is the probability that exactly 16 of the pieces of mail are delivered the next day?

(c) What is the probability that fewer than 16 of the pieces of mail are delivered the next day?

Solution

Binomial distribution used

p=20

P=0.85

P(X=x) = (nCx) px (1-p)n-x

P(X=20) = (20C20) 0.85²⁰ (1-0.85)^20-20   =0.85²⁰

P( x=20) =0.0387( using binomial calculator)

P( x=16) =0.1821 ( using binomial calculator)

P( x<16) = 0.1702 ( using binomial calculator)