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:

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Now, in the Left Cut Off and Right Cut Off boxes (bottom left corner of the applet) enter the numbers 5 and 8 respectively. What do you observe?

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 <math? P(A)=0.346653, P(B)=0.627840, P(C)=0.025507$.</math>

Example 2:

Suppose a lot of size \(N\) is accepted if it contains no more than \(c\) defective components. A production manager selects at random a sample of \(n\) components from this lot and determines the number of defective components. If he finds more than \(c\) defective components then the lot is rejected, otherwise it is accepted. Answer the following questions:

a. Suppose the manager wants to choose between two lot sizes\[N=500\] or \(N=1000\). Both lots will contain \(1 \%\) defective components and he will sample in both cases \(n=5 \%\) of the lot. Which sampling scheme will have a higher probability of falsely rejecting the lot if \(c=0\)? Use SOCR and print the two snapshots.

b. Repeat (a) with \(c=1\). Answer the question using SOCR.

c. Repeat (a) with \(c=1\) and defective rate \(10 \%\). Use SOCR.

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• SOCR Home page: http://www.socr.ucla.edu

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