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mple of 1000 com xin ditions necessary ximation to the b

mple of 1000 com xin ditions necessary ximation to the b

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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4. Suppose 4% of computer chips are defective. What is the probability that in a random sample of 1000 computer chips, at least 50 are defective. Use the normal approximation to the binomial to approximate this probability. Be sure to check the conditions necessary to perform this calculation first.
Transcribed Image Text:4. Suppose 4% of computer chips are defective. What is the probability that in a random sample of 1000 computer chips, at least 50 are defective. Use the normal approximation to the binomial to approximate this probability. Be sure to check the conditions necessary to perform this calculation first.
Expert Solution
Step 1

According to the sum, We have to use the normal approximation to the binomial to approximate this probability.

4% of the computer chips are defective. So,p=the event of success=0.04.

Then q=the event of failure=1-p=1-0.04=0.96

A random sample of 1000 is taken. n=1000.

So, the necessary conditions are, np ≥5 and nq≥5.

Here, np=1000*0.04=40 and nq=1000*0.96=960, both are greater than 5.

So, to use the normal approximation to the binomial, we have, 

μ=np=40 σ=npq=1000×0.04×0.96=38.4  

Let X be a random variable that follows normal distribution representing the computer chips.

X~N(40,38.42)

Z=X-4038.4~N(0,1)

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