As a quality control manager, you are responsible for checking the quality level

Question

As a quality control manager, you are responsible for checking the quality level of AC adapters for tablet PCs that your company manufactures. You must reject a shipment if you find 5 defective units. Suppose a shipment of 48 AC adapters has 8 defective units and 40 non-defective units. Complete parts (a) through (d) below assuming you sample 13 AC adapters.

a) What is the probability that there will be no defective units in the shipment?

b)What is the probability that there will be at least 1 defective unit in the shipment?

c) What is the probability that there will be 4 defective units in the shipment?

d)What is the probability that the shipment will be accepted?

Explanation / Answer

Answer:

As a quality control manager, you are responsible for checking the quality level of AC adapters for tablet PCs that your company manufactures. You must reject a shipment if you find 5 defective units. Suppose a shipment of 48 AC adapters has 8 defective units and 40 non-defective units. Complete parts (a) through (d) below assuming you sample 13 AC adapters.

Hypergeometric distribution used.

N=48, N1=8, n=13

a) What is the probability that there will be no defective units in the shipment?

P( x=0) = 0.0624

b)What is the probability that there will be at least 1 defective unit in the shipment?

P( x1) = 1-P( x=0) = 1- 0.0624

= 0.9376

c) What is the probability that there will be 4 defective units in the shipment?

P( x=4) = 0.0992

d)What is the probability that the shipment will be accepted?

P( x4) = 0.9748

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