SOCR EduMaterials Activities More Examples

\noindent {\bf 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]

\noindent We can use the formula and compute \( P(A) = P(X \ge 9) = \sum_{x=9}^{12} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots \) \( P(b) = P(5 \le X \le 8) = \sum_{x=5}^{8} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots <math> <math> P(A) = P(X < 5) = \sum_{x=0}^{4} {12 \choose x} 0.65^x 0.35^{12-x}=\cdots <math> Or, much easier use SOCR... Here is the distribution of the number of unbruised peaches among the 12 selected: \noindent Now that we know how to use the formula, let's use the SOCR applet to answer these questions. After we enter $n=12$ and $p=0.65$ we get the distribution below: \begin{figure}[h] \includegraphics[height=2.6in, width=5.5in]{peaches1.jpg} \end{figure} \noindent In the {\it Left Cut Off} and {\it Right Cut Off} boxes (left down corner of the applet) enter the numbers 5 and 8 respectively. What do you observe? \begin{figure}[h] \includegraphics[height=2.6in, width=5.5in]{peaches2.jpg} \end{figure} \noindent The distribution is divided into three parts. The left part (less than 5), the right part (above 8), and the between part (between 5 and 8 included). All the SOCR distributions applets are designed in the same way. From the applet the probabilities are $P(A)=0.346653, P(B)=0.627840, P(C)=0.025507$.\)