SOCR EduMaterials Activities More Examples

From Socr

(Difference between revisions)
Jump to: navigation, search
Line 43: Line 43:
c.  Repeat (a) with <math>c=1</math> and defective rate <math>10 \%</math>.  Use SOCR.
c.  Repeat (a) with <math>c=1</math> and defective rate <math>10 \%</math>.  Use SOCR.
 +
 +
 +
 +
<hr>
 +
* SOCR Home page: http://www.socr.ucla.edu
 +
 +
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_More_Examples_Distributions}}

Revision as of 07:23, 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:



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.





Translate this page:

(default)

Deutsch

Español

Français

Italiano

Português

日本語

България

الامارات العربية المتحدة

Suomi

इस भाषा में

Norge

한국어

中文

繁体中文

Русский

Nederlands

Ελληνικά

Hrvatska

Česká republika

Danmark

Polska

România

Sverige

Personal tools