A major pharmaceutical company produces a drug used in the treatment of arthriti

Question

A major pharmaceutical company produces a drug used in the treatment of arthritis at a facility in the Northeastern United States. Periodically, its production process must be evaluated to ensure that it meets FDA requirements. Out from the process is tested independently at two different laboratory facilities. At the first laboratory facility, testing is conducted using equipment that analyzes a sample of 25 units from the production facility. If more than three of the united fail the test, the sample is said to "fail" and the laboratory recommends that the production process at the production facility be halted until the process can be recalibrated. Historically, the probability that analysis will reveal a problem has been 1% at this first laboratory facility. At the second laboratory, the probability that a unit will pass the analysis has been 97%. This facility tests samples of 30 units, and recommends that the facility continue operation only if more than 28 of the test units pass testing.

A) What is the probability that during any given evaluation period, unanimous support is given by the testing facilities for continuing the production process?

** Please make sure you include the calculations, formulas, and any explaination on how to do this problem. Just showing I answer I can't figure out how to do the problem properly. Here are the questions

Explanation / Answer

P(passing the test from first testiing facility)

= P(0 fail) + P(1 fail) + P(2 fails) + P(3 fails)

= 0.9925 + 25x0.01x0.9924 + 25C2x0.012x0.9923 + 25C3x0.013x0.9922 = 0.9999

P(passing the test from testing facility 2)

= P(29 pass) + P(30 pass)

= 30x0.9729x0.03+ 0.9730

= 0.773

For getting unanimus support from both testing facilities, the probability is 0.9999x0.773 = 0.7729

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