Answered: A glass manufacturer finds that 1 in…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 41E

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Question

A glass manufacturer finds that 1 in every

1000

glass items produced is warped. Find the probability that (a) the first warped glass item is the

11th item produced, (b) the first warped item is the first, second, or third item produced, and (c) none of the first 10 glass items produced are defective.

Expert Solution

Step 1

Given Information:

A glass manufacturer finds that 1 in every 1000 glass items produced is warped.

That is: $p = \frac{1}{1000} = 0.001$

Geometric distribution is used when we are interested in the occurrence of the first success.

Formula:

$P (x) = {(1 - p)}^{x - 1} p$

In this case, we are interested in the first success (defective) and so, we use Geometric distribution.

(a) To find the probability that the first warped glass item is the 11th item produced:

Required probability:

$\begin{array}{rcl} P (11) & = & {(1 - 0.001)}^{11 - 1} (0.001) \\ = & {(0.999)}^{10} (0.001) \\ = & 0.0009900448802 \\ \approx & 0.00099 \end{array}$

Thus, probability that the first warped glass item is the 11th item produced is 0.00099

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