Question

This assignment has a value of 10 points. You will have two (2) questions to answer and one (1) attempt to send this assignment. Refer to the calendar in Blackboard for due dates. Your calendar is available under the Tools menu > Calendar. Once you have built the Excel tables, with all the changes in different tables, and answered all the questions you have to send the work (Excel sheets and answered questions) to the professor using the Attach File function in Black Board to attach your document and send it to the professor. To use the Attach File enter the Course Content in Black Board. Select the Assignment Module 5, attach the file and submit. Solve the following problem and compute the probability of the Binomial and Poisson distributions. What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2

Answer 1

0.0337 = 3.37% probability of finding two defects.

Explanation:

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.

What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2?

This is
`P(X = 2)`, with
`n = 30` and
`p = 0.2`. So

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

`P(X = 30) = C_(30,2).(0.2)^(2).(0.8)^(28) = 0.0337`

0.0337 = 3.37% probability of finding two defects.