SOCR EduMaterials Activities More Examples

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Revision as of 22:40, 8 July 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:

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 $P (A) = 0.346653, P (B) = 0.627840, P (C) = 0.025507.$

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 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.

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

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@@ Line 31: / Line 31: @@
-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>
+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>
@@ Line 38: / Line 38: @@
 Suppose a lot of size <math>N</math> is accepted if it contains no more than <math>c</math> defective components.   A production manager selects at random a sample of <math>n</math> components from this lot and determines the number of defective components. If he finds more than <math>c</math> 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:  <math>N=500</math> or <math>N=1000</math>.  Both lots will contain <math>1 \%</math> defective components and he will sample in both cases <math>n=5 \%</math> of the lot.  Which sampling scheme will have a higher probability of falsely rejecting the lot if <math>c=0</math>?  Use SOCR and print the two snapshots.
+a.  Suppose the manager wants to choose between two lot sizes:  <math>N=500</math> or <math>N=1000</math>.  Both lots will contain <math>1 \%</math> defective components and he will sample in both cases <math>n=5 \%</math> of the lot.  Which sampling scheme will have a higher probability of rejecting the lot if <math>c=0</math>?  Use SOCR and print the two snapshots.
 b.  Repeat (a) with <math>c=1</math>.  Answer the question using SOCR.

SOCR EduMaterials Activities More Examples

From Socr

Revision as of 22:40, 8 July 2007

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