Upon completion of this assignment you will be able to

Objectives:

Upon completion of this assignment you will be able to:

1. Calculate probabilities for various distributions.

Rational:

Much of control chart and acceptance sampling theory is based on probability.

Fundamentals of Probability, Chapter 8 [25 points]

1. [5 points] A finite lot of 40 digital watches includes30% nonconforming units. Using the hypergeometric distribution, what is the probability that a sample of 6 will contain 3 nonconforming watches? Show your work.
2.  [5 points] Find the probability, using the binomial distribution, of obtaining 4 or more nonconforming units when sampling 30 computers from a batch known to be 10% nonconforming. Show your work.
3. [5 points] An injection molding machine produces golf tees that are 20.0% nonconforming. Using the normal distribution as an approximation to the binomial, find the probability that, in a random sample of 360 golf tees, 65 or less are nonconforming. Show your work.
4. [5 points]A sample of 10 printed labels is selected from a process that is 15% nonconforming. What is the probability of 2 nonconforming labels in the sample? Use the Poisson distribution. Show your work.
5. [5 points]Using Excel, construct one graph showing the entire distribution from 0 to 10 for:
1. Hypergeometric, where n = 10, N = 50, D = 15
2. Binomial, where n = 50 and p = 0.06
3. Poisson, where np = 4