The Grapes of China The Chinese wine industry has become very large. However, there are many quality control problems.45 Wine batches are systematically examined for alcohol content, total sugar,...

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The Grapes of China The Chinese wine industry has become very large. However, there are many quality control problems.45 Wine batches are systematically examined for alcohol content, total sugar, volatile acid, and other food additives. Suppose the Yantai Best Cellar Consulting Company claims that only 3% of all bottles are unqualified, or defective. Suppose six bottles of Yantai wine are selected at random.

a. What is the probability that none of the six bottles will be unqualified?

b. What is the probability that at least one of the bottles will be unqualified?

c. Suppose all six bottles are unqualified. Do you believe the company’s claim? Justify your answer.

Answered Same DayDec 25, 2021

Answer To: The Grapes of China The Chinese wine industry has become very large. However, there are many quality...

Robert answered on Dec 25 2021

123 Votes

Let X denote number of unqualified in n = 6 independent bottles, where each
has a probability p = 0.03
We denote this by:
X ∼ Binomial(n = 6, p = 0.03)
A P (X = 0), n = 6, p = 0.03
P (X = 0) =
(
n
x
)
px(1 − p)n−x =
(6
0
)
(0.03)0(1 − 0.03)6−0 = 1 ∗ (0.03)0(0.97)6 =
0.832972 ≈ 0.832972 ≈ 0.833
P (X = 0) = 0.833
Using excel function BinomDist(0,6,0.03,false) or TI-83/84 function
binompdf(6,0.03,0), exact answer is...

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The Grapes of China The Chinese wine industry has become very large. However, there are many quality control problems.45 Wine batches are systematically examined for alcohol content, total sugar,...

Answer To: The Grapes of China The Chinese wine industry has become very large. However, there are many quality...

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