Question

In: Statistics and Probability

A laptop manufacturing company has implemented a 2-step process to test the quality of each production...

A laptop manufacturing company has implemented a 2-step process to test the quality of each production batch. In the first step, a technician randomly selects 15 laptops from the batch and determines whether they meet specifications. The batch is considered acceptable provided no more than 1 laptop fails to meet specifications. Otherwise, the entire batch must be tested in the second step. Historical data shows that 95% of the laptops produced adhere to specifications. Discuss the following:

What are the 4 characteristics of a binomial experiment?
Can we use a binomial distribution to model this process?
What is the probability that the entire batch unnecessarily has to be tested if in fact 95% of its laptops conform to specifications? (Hint: Use Excel’s =BINOMDIST() function to find the probability.)
What is the probability that the batch is incorrectly accepted if only 75% of its laptops conform to specifications?

Expert Solution

(a) The 4 characteristics of a binomial experiment are,

· There are fixed number of trials

· Each trial is independent of the other trials

· The outcomes can be categorized into two categories, "success" and "failure".

· The probability of success is fixed in each trial.

(b) In this case 15 laptops are selected so number of trials is fixed,

The laptops are often categorized nearly as good or defective,

Each laptop is independent of others, the probability of getting a defective laptop is fixed.

So all 4 conditions are satisfied and thus it are often taken as a binomial distribution model.

(c) The entire batch has to be tested if the number of defective is more than 1.

So the excel command would be "1-BINOMDIST(1,15,0.05,TRUE)".

The obtained probability is 0.17095.

(d) Incorrectly accepted means, the defective rate is 0.25 but the batch is accepted i.e.

number of defectives is less than or equal to 1.

Required probability can be found using the excel command "BINOMDIST(1,15,0.25,TRUE)"

which is giving the probability as 0.08018.

orchestra answered 2 years ago

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