John Sperry, president of Federal Express, is proud of their next day service. H

Question

John Sperry, president of Federal Express, is proud of their next day service. Historically, on average only 4 ½% of all next day service packages arrive late. In a quarterly report requested by the Board of Directors, Mr. Sperry is asked to find the probability that less than three of the projected 200 packages to be delivered for the following week will arrive late.

I have received various answers from different experts and I am confused as to which is the correct one. Please review and help me understand the correct answer and the correct theory/formula used.

Answer 1:

According to Binomial Probability Function:

P= probability of a package arrive late = 0.045

n =number of packages = 200

x = packages that arrives late

x ˜ b(n,p) à x ˜ b (200, 0.045)

P ( X <= xi) =

P(x < 3 ) =

P( x < 3 ) = 0.0055

The probability that less than three of the projected 200 packages to be delivered for the following week will arrive late is 0.0055

Answer 2:

Answer 3:

Answer 4

Solution: The probability that less than three of the projected 200 packages to be delivered for the following week will arrive late is 0.005469. Probability of parcels arri iving late 30.045 Total number of packages 3200 ess than 3 By using Binomial distribution theorem X, n P(x

Explanation / Answer

here all are correct, it depends on which calculator u r using and weather u want precise result or approximate.

here probabilty is independent and equal for number of days and number of trails are fixed which is N=200

therefore above is a binomial distribution.

from which Answer 1 and 2 are correct.

for if you want poisson approximation of distribution you can use Answer 3 or 4.

please reply if needed further clarification

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