Question

Question 17 The probability that a customer's order is not shipped on time is 0.02. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all are shipped on time

Answer 1

0.941192 = 94.1192% probability that all are shipped on time

Explanation:

For each order, there are only two possible outcomes. Either they are shipped on time, or they are not. The probability of an order being shipped on time is independent of other orders. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

The probability that a customer's order is not shipped on time is 0.02.

So 1 - 0.02 = 0.98 probability of being shipped on time, which means that
`p = 0.02`

A particular customer places three orders

This means that
`n = 3`

(a) What is the probability that all are shipped on time

This is
`P(X = 3)`.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 3) = C_(3,3).(0.98)^(3).(0.02)^(0) = 0.941192`

0.941192 = 94.1192% probability that all are shipped on time