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# The following table summarizes 204 endothermic reactions ISBN: 9781118539712 55

## Solution for problem 50E Chapter 2.1

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 A B.

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 A B={12,44}.

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

Thus, the number of reactions in the event A B 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

Step 5 of 6

##### ISBN: 9781118539712

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