mple of 1000 com xin ditions necessary ximation to the b

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
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 nq5.

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)

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman