Concept explainers
(a)
Meaning for F and M assumed as independent random variables in context.
(a)

Answer to Problem 59E
Randomly selected female student F and randomly selected male student M does not affect each other’s SSHA score.
Explanation of Solution
Given information:
F and M are independent random variables.
For F :
Standard deviation,
For M :
Mean,
Standard deviation,
F : SSHA score of a randomly selected female student at a large university
M : SSHA score of a randomly selected female student at a large university
We know that
F and M are independent random variables.
This implies
In any way, the SSHA score of the female student F does not affect the SSHA score of the male student M .
Similarly,
In any way, the SSHA score of the male student M does not affect the SSHA score of the female student F .
(b)
Interpretation and calculation of standard deviation of the difference in scores.
(b)

Answer to Problem 59E
On an average, the difference between the female and male SSHA scores deviates by approx. 44.8219 points from the mean difference of 15 points.
Explanation of Solution
Given information:
F and M are independent random variables.
For F :
Mean,
Standard deviation,
For M :
Mean,
Standard deviation,
F : SSHA score of a randomly selected female student at a large university
M : SSHA score of a randomly selected female student at a large university
Now,
Meandifference of the mean of both male and female SSHA scores:
When the random variables are independent, the variance of the difference is equal to the sum of their variances.
We also know that
The standard deviation is the square root of the variance:
On an average, the difference between the female and male SSHA scores deviates by approx. 44.8219 points from the mean difference of 15 points.
(c)
Whether it is possible to find the probability for the randomly selected female student has a higher SSHA score than the randomly selected male student.
(c)

Answer to Problem 59E
No, because the distributions of F and M are not known.
Explanation of Solution
Given information:
F and M are independent random variables.
For F :
Mean,
Standard deviation,
For M :
Mean,
Standard deviation,
From Part (b),
We came to know that
The difference F - M had mean of 15 points and standard deviation of approx. 44.8219 points.
Since the distribution of F or the distribution M is not known.
Thus,
The distribution of the difference F - M cannot be determined.
Hence,
It is impossible to determine the probability that the female student scores a higher SSHA score than the male student.
Chapter 6 Solutions
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