Refer to Exercise 17 for the definition of a k out of n

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

Problem 18E Chapter 4.2

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 0 386 Reviews
13
5
Problem 18E

Refer to Exercise 17 for the definition of a k out of n system. For a certain 4 out of 6 system, assume that on a rainy day each component has probability 0.7 of functioning, and that on a nonrainy day each component has probability 0.9 of functioning.

a. What is the probability that the system functions on a rainy day?

b. What is the probability that the system functions on a nonrainy day?

c. Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?

Step-by-Step Solution:
Step 1 of 3

Solution 18E

Step1 of 4:

Let us consider a random variable X it presents the number of components function properly on a rainy season.Then X follows binomial distribution with parameters “n and p” that is X B(n, p),

The probability mass function of binomial distribution is given by

, x = 0,1,2,...,n.

Where,

n = sample size

   = 6

x = random variable

p = probability of success

   = Probability that the each component is function on rainy season

   = 0.70

q = 1 - p (probability of failure)

   = 1 - 0.70

   = 0.30

Here our goal is:

a.We need to find the probability that the system functions on a rainy day.

b.We need to find the probability that the system functions on a non-rainy day.

c.We need to find the probability that the system will function tomorrow, by assuming that the probability of rain tomorrow is 0.20.

Step2 of 4:

a).

We have n = 6 and p = 0.70.

P(The system functions on a rainy day) = P(X 4)

                                                                = P(X = 4) + P(X = 5) + P(X = 6)

                                                                = {++

                                                                         }

                                                                = 15(0.2401)(0.09)+6(0.1680)(0.30)+1(0.1176)(1)

                                                                = 0.3241+0.3024+0.1176

                                                                = 0.7441

Hence, P(The system functions on a rainy day) = 0.7441.

Step3 of 4:

b).

We have n = 6 and...

Step 2 of 3

Chapter 4.2, Problem 18E is Solved
Step 3 of 3

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

×
Log in to StudySoup
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 4.2 - Problem 18e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 4.2 - Problem 18e
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