Vendor A supplies parts, each of which has probability

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Problem 1E Chapter 4.12

Statistics for Engineers and Scientists | 4th Edition

  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 0 358 Reviews
22
0
Problem 1E

Vendor A supplies parts, each of which has probability 0.03 of being defective. Vendor B also supplies parts, each of which has probability 0.05 of being defective. You receive a shipment of 100 parts from each vendor.

a. Let X be the number of defective parts in the shipment from vendor A and let Y be the number of defective parts in the shipment from vendor B. What are the distributions of X and Y?

b. Generate simulated samples of size 1000 from the distributions of X and Y.

c. Use the samples to estimate the probability that the total number of defective parts is less than 10.

d. Use the samples to estimate the probability that the shipment from vendor A contains more defective parts than the shipment from vendor B.

e. Construct a normal probability plot for the total number of defective parts. Is this quantity approximately normally distributed?

Step-by-Step Solution:

Step 1 of 4:

Vendor A suppliers parts which has probability 0.03 of being defective.

Vendor B suppliers parts which have probability 0.05 of being defective.

There is a shipment of 100 parts from each vendor.

Let X be the number of defective parts in the shipment from the vendor and Y be the number of defective parts in the shipment from vendor B.

Step 2 of 4:

We have to find the distribution of X and Y.

 

According to the definition of binomial distribution:

It a total of n trials conducted,then

The trials must be independent. Each trials have same success probability P . Each trial have only two possibilities.

Since from the given data it is clear that each parts can be either defective or nondefective,With a given probabilities of being defective.

P(X) = 0.03, P(Y)= 0.05

And each trials are independent.  We assume that the number of defective as the number of success .

   X ~ B(100, 0.03) and Y~B(100,0.05)

That means both X and Y follows a binomial distribution.

 

      (b)   We have to generate a random sample of 100 from the distribution of X and Y.

      From the given data it is clear that the variables X and Y follows binomial distribution.

     By using software like minitab we can generate the random sample for any distribution as:

 Calc- random data- distribution - parameters (with sample size)- ok( store the data in column 1 and column 2).

   

The generated sample can be different.

Step 3 of 4

Chapter 4.12, Problem 1E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4th
Author: William Navidi
ISBN: 9780073401331

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Vendor A supplies parts, each of which has probability

×
Log in to StudySoup
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 4.12 - Problem 1e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 4.12 - Problem 1e
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here