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The following table summarizes 204 endothermic reactions

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 50E Chapter 2.1

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 50E Problem 50E

The following table summarizes 204 endothermic reactions involving sodium bicarbonate.

Let A denote the event that a reaction’s final temperature is 271 K or less. Let B denote the event that the heat absorbed is below target. Determine the number of reactions in each of the following events.

Step-by-Step Solution:

Step 1 of 6:

The data regarding the summaries of 204 endothermic reactions is given.

Final Temperature conditions

             Heat absorbed (cal)

Below target

Above target

266K

12

40

271K

44

16

274K

56

36

Also, it is given that  A denotes the event that a reaction's final  temperature is 271K or less and B denotes the event that heat absorbed is below target.

Using this we need to find the required values.

Step 2 of 6:

(a)

Here we have to determine the number of reactions corresponding to event AB.

A=Reaction’s final temperature is 271K or less.

So

A={12,40,44,16}

B=Heat absorbed is below target

So

B-{12,44,56}

Hence AB={12,44}.

Then the number of reactions in this event become 44+12=56 reactions.

Thus, the number of reactions in the event AB is 56 reactions.

Step 3 of 6:

(b)

Here we have to determine the number of reactions in the event

denotes the event that the reaction’s final temperature is more than 271K.

So, the number of reactions in the set become 56+36=92 reactions.

Thus, the number of reactions in the event are 92 reactions.

Step 4 of 6

Chapter 2.1, Problem 50E is Solved
Step 5 of 6

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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The following table summarizes 204 endothermic reactions

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