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Chapter 5: Q5.4-3E (page 275)

Suppose that the number of defects on a bolt of cloth produced by a certain process has the Poisson distribution with a mean of 0.4. If a random sample of five bolts of cloth is inspected, what is the probability that the total number of defects on the five bolts will be at least 6?

Short Answer

Expert verified

The probability of defects on the five bolts will be at least 6 is 0.0165.

Step by step solution

01

Given information

The number of defects on a bolt of cloth follows a Poisson distribution with a mean of 0.4.

02

Compute the probability

Let the total number of defects on a bolt of cloth be denoted by X, which is produced by a certain process.

Then the variable X has a Poisson distribution with a mean of 0.4.

Let five bolts of cloth be inspected.

The sum of the numbers of defects on five bolts of cloth will follow a Poisson distribution with a mean \(\left( {0.4 \times 5} \right) = 2\).

The probability of defects on the five bolts will be at least 6 is

\(\begin{array}{}P\left( {X \ge 6} \right) = 0.0120 + 0.0034 + 0.0009 + 0.0002\\ = 0.0165\end{array}\)

(Referring to the table of Poisson probabilities on page number 857 for the answer)

Therefore, the probability of defects on the five bolts at least 6 is 0.0165.

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