Problem 114E
Consider the endothermic reactions in Exercise 332. 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?
332. 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.
Answer
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