SOCR EduMaterials Activities More Examples

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Example 1:
Example 1:
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From a large shipment of peaches, 12 are selected for quality control.  Suppose that in this particular shipment only $65 \%$ of the peaches are unbruised.  If among the 12 peaches 9 or more are unbruised the shipment is classified A.  If between 5 and 8 are unbruised the shipment is classified B.  If fewer than 5 are unbruised the shipment is classified C.  Compute the probability that the shipment will be classified A, B, C. \\[.1in]
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From a large shipment of peaches, 12 are selected for quality control.  Suppose that in this particular shipment only <math>65 \%</math> of the peaches are unbruised.  If among the 12 peaches 9 or more are unbruised the shipment is classified A.  If between 5 and 8 are unbruised the shipment is classified B.  If fewer than 5 are unbruised the shipment is classified C.  Compute the probability that the shipment will be classified A, B, C.
We can use the formula and compute
We can use the formula and compute
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<math>
<math>
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P(b) = P(5 \le X \le 8) = \sum_{x=5}^{8} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots
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P(B) = P(5 \le X \le 8) = \sum_{x=5}^{8} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots
</math>
</math>
<math>
<math>
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P(A) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots
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P(C) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots
</math>
</math>
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Or, much easier use SOCR...  Here is the distribution of the number of unbruised peaches among the 12 selected:
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Or, much easier using SOCR...   
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\noindent Now that we know how to use the formula, let's use the SOCR applet to answer these questions.  After we enter $n=12$ and $p=0.65$ we get the distribution below:
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Here is the distribution of the number of unbruised peaches among the 12 selected.  After we enter <math>n=12</math> and <math>p=0.65</math> we get the distribution below:
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\begin{figure}[h]
 
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\includegraphics[height=2.6in, width=5.5in]{peaches1.jpg}
 
\end{figure}
\end{figure}

Revision as of 07:05, 1 June 2007

Example 1:

From a large shipment of peaches, 12 are selected for quality control. Suppose that in this particular shipment only 65 \% of the peaches are unbruised. If among the 12 peaches 9 or more are unbruised the shipment is classified A. If between 5 and 8 are unbruised the shipment is classified B. If fewer than 5 are unbruised the shipment is classified C. Compute the probability that the shipment will be classified A, B, C.

We can use the formula and compute


P(A) = P(X \ge 9) = \sum_{x=9}^{12} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots


P(B) = P(5 \le X \le 8) = \sum_{x=5}^{8} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots


P(C) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots

Or, much easier using SOCR...

Here is the distribution of the number of unbruised peaches among the 12 selected. After we enter n = 12 and p = 0.65 we get the distribution below:

\end{figure}

\noindent In the {\it Left Cut Off} and {\it Right Cut Off} boxes (left down corner of the applet) enter the numbers 5 and 8 respectively. What do you observe?

\begin{figure}[h] \includegraphics[height=2.6in, width=5.5in]{peaches2.jpg} \end{figure}

\noindent The distribution is divided into three parts. The left part (less than 5), the right part (above 8), and the between part (between 5 and 8 included). All the SOCR distributions applets are designed in the same way. From the applet the probabilities are $P(A)=0.346653, P(B)=0.627840, P(C)=0.025507$.</math>

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