Difference between revisions of "SOCR EduMaterials Activities More Examples"
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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] | 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] | ||
| − | + | We can use the formula and compute | |
| + | |||
<math> | <math> | ||
P(A) = P(X \ge 9) = \sum_{x=9}^{12} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots | P(A) = P(X \ge 9) = \sum_{x=9}^{12} {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 | 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> | ||
P(A) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots | P(A) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots | ||
</math> | </math> | ||
| + | |||
Or, much easier use SOCR... Here is the distribution of the number of unbruised peaches among the 12 selected: | Or, much easier use SOCR... Here is the distribution of the number of unbruised peaches among the 12 selected: | ||
\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: | \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: | ||
Revision as of 02:07, 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. \\[.1in]
We can use the formula and compute
\( P(A) = P(X \ge 9) = \sum_{x=9}^{12} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots \)
\( P(b) = P(5 \le X \le 8) = \sum_{x=5}^{8} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots \)
\( P(A) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots \)
Or, much easier use SOCR... Here is the distribution of the number of unbruised peaches among the 12 selected: \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:
\begin{figure}[h] \includegraphics[height=2.6in, width=5.5in]{peaches1.jpg} \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>
