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Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 3.6 - Problem 114e
Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 3.6 - Problem 114e

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# Consider the endothermic reactions in Exercise 3-32. A ISBN: 9781118539712 55

## Solution for problem 114E Chapter 3.6

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 114E

Problem 114E

Consider the endothermic reactions in Exercise 3-32. A total of 20 independent reactions are to be conducted.

(a) What is the probability that exactly 12 reactions result in a final temperature less than 272 K?

(b) What is the probability that at least 19 reactions result in a final temperature less than 272 K?

(c) What is the probability that at least 18 reactions result in a final temperature less than 272 K?

(d) What is the expected number of reactions that result in a final temperature of less than 272 K?

3-32. The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows:

 Final Temperature Conditions Number of Reactions 266 K 48 271 K 60 274 K 92

Calculate the probability mass function of final temperature.

Step-by-Step Solution:

Step 1 of 4

(a)

Consider the endothermic reactions in given below the table.

A total of independent reactions is to be conducted.

 Final Temperature Conditions Number of Reactions 266 K 48 271 K 60 274 K 92

We are asked to find the probability that exactly reactions result in a final temperature less than .

Hence the probability mass function PMF is according to the definition of PMF present in the table given below.

 Final Temperature Conditions Number of Reactions PMF 266 K 48 271 K 60 274 K 92 Let denote the number of the reactions result in a final temperature less than .

We need to find Hence follows a binomial distribution which we can write,

The random variable that equals the number of trials that result in a success is a binomial random variable with parameters The probability mass function (PMF) of is, ………………(1)

The probability that the reactions result in a final temperature less than is from the table,  We have given Hence the substitute the above values into equation (1),  Hence the probability that exactly reactions result in a final temperature less than is Step 2 of 4

Step 3 of 4

##### ISBN: 9781118539712

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