a.
Find the probability that the concentration is greater than 0.5.
a.
Answer to Problem 22E
The probability of the concentration is greater than 0.5 is 0.269.
Explanation of Solution
Given info:
The concentration of a reactant is a random variable with probability density
Calculation:
Let X be a continuous random variable with probability density function
Let X is the concentration of a reactant.
The probability that the concentration is greater than 0.5can be obtained as,
Thus, the probability of the concentration is greater than 0.5 is 0.269.
b.
Find the
b.
Answer to Problem 22E
The mean concentration is 0.3435.
Explanation of Solution
Calculation:
Mean:
Let X be a continuous random variable with probability density function
The mean concentration can be obtained as,
Upper limit: if
Lower limit: if
Thus, the mean concentration is 0.3435.
c.
Find the probability that the concentration is within
c.
Answer to Problem 22E
The probability that the concentration is within
Explanation of Solution
Calculation:
The probability that the concentration is within
Thus, the probability that the concentration is within
d.
Find the standard deviation of the concentration.
d.
Answer to Problem 22E
The standard deviation of the concentration is 0.2627.
Explanation of Solution
Calculation:
Variance:
Let X be a continuous random variable with probability density function
Standard deviation:
The standard deviation is of the continuous variable is,
The variance of the concentration can be obtained as,
Upper limit: if
Lower limit: if
Thus, the variance of the concentration is 0.04.
The standard deviation of the concentration is,
Thus, the standard deviation of the concentration is 0.2627.
d.
Find the probability that the concentration is within
d.
Answer to Problem 22E
The probability that the concentration is within
Explanation of Solution
Calculation:
The probability that the concentration is within
Thus, the probability that the concentration is within
f.
Find the cumulative distribution function of the concentration.
f.
Answer to Problem 22E
The cumulative distribution function of the concentration is,
Explanation of Solution
Calculation:
Cumulative distribution function:
Let X be a continuous random variable with probability density function
For
For
For
Thus, the cumulative distribution function of the concentration is,
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Chapter 2 Solutions
Statistics for Engineers and Scientists
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill