SOCR EduMaterials Activities More Examples
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:
Now, 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?
\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>
