An electric component for a medical xray unit is produced in lotsof size n=30. A

Question

An electric component for a medical xray unit is produced in lotsof size n=30. An acceptance testing procedure is used by thepurchaser to protect against lots that contain too manynonconforming components. The procedure consists of selecting 6 components at random from the lot (without replacement) and testing them. If none of the components is nonconforming, the lot is accepted. If the lot contains two non-conforming units what is the probabilit of the lot acceptance?

a) ID the distribution. (I think it's binomial)

b) calculate the probability to 4 decimal places.

Explanation / Answer

a)
Yes this is binomial distribution.

b)
If the lot contains two non-conforming units and if we want lot to be accepted, the 6 componenets selected should not include those any of 2 non-conforming components.

selecting 6 components from 28 good components can be done in 28C6 ways

Hence required probability = 28C6/30C6 = 0.6345

We can also use the binomial distribution formula with p = 2/30 and n=6
P(X = 0) = 6C0*(2/30)^0 * (28/30)^6 = 0.6610

We see the difference in two values because binomial distribution considers with replacement. Hence we get highter probability.

Probability calculated first i.e. 0.6345 is more accurate.

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