A manufacturing company produces an extremely expensive (about $480,000) militar

Question

A manufacturing company produces an extremely expensive (about $480,000) military-grade laser product that requires a tremendous amount of accuracy in order for the product to adhere to the military’s requirements. The precision requirements are so significant, that fully 7% of the completed units are found to be below specification requirements upon evaluation, and therefore have to be sent back for evaluation and rebuilding. If the company produces 6 units every month, what it the likelihood of all 6 of these units being fully up to specification and ready to ship to the client? What statistical assumption discussed in lecture must be made in order to come up with this solution?   

Explanation / Answer

A manufacturing company produces an extremely expensive (about $480,000) military-grade laser product that requires a tremendous amount of accuracy in order for the product to adhere to the military’s requirements. The precision requirements are so significant, that fully 7% of the completed units are found to be below specification requirements upon evaluation, and therefore have to be sent back for evaluation and rebuilding. If the company produces 6 units every month, what it the likelihood of all 6 of these units being fully up to specification and ready to ship to the client? What statistical assumption discussed in lecture must be made in order to come up with this solution?

7% of the completed units are found to be below specification requirements.

93% are met the specification

Binomial distribution is used.

p=0.93

n=6

P(X=x) = (nCx) px (1-p)n-x   

P(X=6) = (6C6) 0.936 (1-0.93)6-6   

P(X = 6) = 0.64699

Assumptions of the binomial distribution

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