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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Quality Control An assembly line that manufactures fuses for automotive use is checked every hour to ensure the quality of the finished product. Ten fuses are selected randomly, and if any one of the ten is found to be defective, the process is halted and the machines are recalibrated. Suppose that at a certain time 5 % of the fuses being produced are actually defective. What is the probability that the assembly line is halted at that hour's quality check?

To determine

To find:

The probability that the assembly line is halted at the time of quality check.

Explanation

Given:

Number of trial is 10.

The number of success is 1.

The total defective fuses are 5%.

Approach:

Write the expression for the probability of success in a trial.

P(S)=p

Here, P(S) is the probability of success.

Write the expression to find the probability of failure in a trial.

P(F)=1pq=1p ……(1)

Here, q=P(F) is probability of failure.

Write the expression to find the probability of getting exactly r success in given number of independent trials of the experiment.

P(rsuccessesinntrials)=C(n,r)prqnr …... (2)

Here, n is the number of trial and r is the number of success in the given experiment.

Write the formula to find the number of combinations.

C(n,r)=n!r!(nr)!

Substitute n!r!(nr)! for C(n,r) in equation (2). Then,

P(rsuccessesinntrials)=(n!r!(nr)!)prqnr ……(3).

Calculation:

Consider the probability of success in a trial for given experiment

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Chapter 14 Solutions

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