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 anyone of the ten is found to be defective, the process is halted and the machines are re-calibrated. 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?
Recall that the formula for the binomial probability is given by
$C(n,r) p^r q^{n-r}$
In this case, the probability of success is $p =0.05$ and the probability of failure is $q = 1-p = 0.95$.
To solve this more easily, we will apply the complement to the probability that none of the ten fuses selected are not defective. Thus, the probability that at least one of ten fuses are defective is
$
\begin{equation}
\begin{aligned}
=& 1 - \left[C(10,0) (0.05)^0 (0.95)^{10-0}\right]
\\
\\
=& 1 - [0.5987]
\\
\\
=& 0.4013
\end{aligned}
\end{equation}
$
Sunday, November 6, 2016
College Algebra, Chapter 10, 10.4, Section 10.4, Problem 26
Subscribe to:
Post Comments (Atom)
Why is the fact that the Americans are helping the Russians important?
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book tha...
-
The only example of simile in "The Lottery"—and a particularly weak one at that—is when Mrs. Hutchinson taps Mrs. Delacroix on the...
-
A good thesis statement presents a claim (an interpretive stance on a story that can be defended using textual evidence) and is a position w...
-
The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function y=ab^x plug-in the given x an...
-
What does the hot air balloon symbolize? To the Assad son who buys the hot air balloon, it symbolizes a kind of whimsy that he can afford. B...
-
The play Duchess of Malfi is named after the character and real life historical tragic figure of Duchess of Malfi who was the regent of the ...
-
Allie’s baseball mitt is extremely important to Holden in The Catcher in the Rye. It is a symbol of Allie since it was important to his brot...
No comments:
Post a Comment