Difference between revisions of "SOCR EduMaterials Activities More Examples"
| Line 1: | Line 1: | ||
Example 1: | Example 1: | ||
| − | From a large shipment of peaches, 12 are selected for quality control. Suppose that in this particular shipment only | + | 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 | ||
| Line 10: | Line 10: | ||
<math> | <math> | ||
| − | P( | + | 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( | + | P(C) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots |
</math> | </math> | ||
| − | Or, much easier | + | Or, much easier using SOCR... |
| − | + | ||
| + | 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: | ||
| − | |||
| − | |||
\end{figure} | \end{figure} | ||
Revision as of 02:11, 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>
