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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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According to results from the analysis of chocolate bars

Chapter 4, Problem 123E

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QUESTION:

Problem 123E

According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume that the number of fragments follows a Poisson distribution.

(a) What is the mean number of grams of chocolate until a fragment is detected?

(b) What is the probability that there are no fragments in a 28.35-gram (one-ounce) chocolate bar?

(c) Suppose you consume seven one-ounce (28.35-gram) bars this week. What is the probability of no insect fragments?

Questions & Answers

QUESTION:

Problem 123E

According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume that the number of fragments follows a Poisson distribution.

(a) What is the mean number of grams of chocolate until a fragment is detected?

(b) What is the probability that there are no fragments in a 28.35-gram (one-ounce) chocolate bar?

(c) Suppose you consume seven one-ounce (28.35-gram) bars this week. What is the probability of no insect fragments?

ANSWER:

Solution

Step 1 of 4

Given that the mean no.of insect fragments was 14.4 in 225 grams

Then in one gram no.of fragments is 14.4/225=0.064

Then

Let X be the no.of grams of chocolate till insect fragment is detected

Here X is exponential random variable

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