Question

Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of 40 components can be viewed as the 40 trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 5%. Suppose a random sample of five items from a recent shipment is tested. Assume that 5% of the shipment is defective and this probability do not change from trial to trial (follows a binomial distribution). What is the probability that four or more items in the sample are defective.

Answer #1

**This is clearly mentioned that the given situation is an
application of BINOMIAL EXPERIMENT.**

**Here , number of trials ,n = 5 items.**

**Probability of component being defective i.e probability
of success ,p = 5%= 0.05**

**let X be the number of defective items out of 5 randomly
selected items.**

**Now we need to find P(X>=4).**

**FORMULA: P(X=x)
= ncx. p^x . q^n-x .**

**here n=5 , X=4, 5 p=0.05, q=1-p = 1-0.05 =
0.95**

**P(X>=4) = P(X=4) + P(X=5)**

**=[5c4 . (0.05)^4 . (0.95)^5-4 ]+[5c5 . (0.05)^5 .
(0.95)^5-5 ]**

**= 0.0000296875 + 0.0000003125**

**= 0.00003 answer.**

**Hence, probability that 4 or more items of the sample
are defective = 0.00003 answer**

Many companies use a quality control technique called acceptance
sampling to monitor incoming shipments of parts, raw materials, and
so on. In the electronics industry, component parts are commonly
shipped from suppliers in large lots. Inspection of a sample of 40
components can be viewed as the 40 trials of a binomial experiment.
The outcome for each component tested (trial) will be that the
component is classified as good or defective. Reynolds Electronics
accepts a lot from a particular supplier...

Many companies use a quality control technique called acceptance
sampling to monitor incoming shipments of parts raw materials and
so on. In the electronics industry, component parts are commonly
shipped from suppliers in large lots. Inspection of a sample
n components can be viewed as the n trials of a binomial
the experiment. That outcome for each component test (trail) will
be that the component is classified as good or defective. Reynolds
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In quality control technique, acceptance sampling is used to
monitor incoming shipment of parts, raw materials, and so on. In
the electronic industry, components parts are commonly shipped from
suppliers in large lots. Reynolds Electronics accepts a lot from a
particular supplier if the defective components in the lot do not
exceed 2%. Suppose a random of 5 items from a recent shipment is
tested.
1. What is the appropriate distribution that can be used here?
Explain why.
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In quality control technique, acceptance sampling is used to
monitor incoming shipment of parts,
raw materials, and so on. In the electronic industry, components
parts are commonly shipped from
suppliers in large lots. Reynolds Electronics accepts a lot from a
particular supplier if the defective
components in the lot do not exceed 2%. Suppose a random of 5 items
from a recent shipment is
tested.
1. What is the appropriate distribution that can be used here?
Explain why.
2. What...

In quality control technique, acceptance sampling is used to
monitor incoming shipment of parts, raw materials, and so on. In
the electronic industry, components parts are commonly shipped from
suppliers in large lots. Reynolds Electronics accepts a lot from a
particular supplier if the defective components in the lot do not
exceed 2%. Suppose a random of 5 items from a recent shipment is
tested.
1. What is the appropriate distribution that can be used here?
Explain why.
2. What...

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