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A certain brand of dinnerware set comes in three colors:

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 2E Chapter 4.1

Statistics for Engineers and Scientists | 4th Edition

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

Statistics for Engineers and Scientists | 4th Edition

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Problem 2E

A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise.

a. Let pX denote the success probability for X. Find pX.

b. Let pY denote the success probability for Y. Find pY.

c. Let pZ denote the success probability for Z. Find pZ.

d. Is it possible for both X and Y to equal 1?

e. Does pZ = pX + py ?

f. Does Z = X + Y ? Explain.

Step-by-Step Solution:

Answer:

Step 1 of 6:

(a)

In this question, we are asked to find the success probability for  and hence .

Given brand of dinnerware has three colors: red, white, and blue.

Customers order the red set =

Customers order the white set  =

Customers order the blue set =

Let if a randomly chosen order is for a red set, let   otherwise.

Let if a randomly chosen order is for a white set, let   otherwise.

Let if a randomly chosen order is for either a red or white set, let   otherwise.

Since given data is in percentage.

We can say out of  customers,  customers ordered the red set.

 

Hence the success probability for () is .

Step 2 of 6:

(b)

In this question, we are asked to find the success probability for and hence .

We can say out of  customers,  customers ordered the red set.

 

Hence the success probability for () is .

Step 3 of 6:

(c)

In this question, we are asked to find the success probability for  and hence .

Since if a randomly chosen order is for either a red or white set, and  otherwise.

Then we can write,

  =

Substitute the values of probabilities from  the above questions,  and  

  =

  =

Hence the success probability for () is .

Step 4 of 6

Chapter 4.1, Problem 2E is Solved
Step 5 of 6

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

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 2E from chapter: 4.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 2E from 4.1 chapter was answered, more than 1950 students have viewed the full step-by-step answer. This full solution covers the following key subjects: let, order, set, red, white. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise.a. Let pX denote the success probability for X. Find pX.________________b. Let pY denote the success probability for Y. Find pY.________________c. Let pZ denote the success probability for Z. Find pZ.________________d. Is it possible for both X and Y to equal 1?________________e. Does pZ = pX + py ?________________f. Does Z = X + Y ? Explain.” is broken down into a number of easy to follow steps, and 143 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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