Concept explainers
Answer to Problem 72E
Probability for the scores differ by 5 or more points in either direction is 0.0768.
Explanation of Solution
Given information:
Mean and standard deviation,
For Fred:
For Leona:
Calculations:
Let
X1 : Fred’s score
X2 : Leona’s score
Then
X1 - X2 is the difference in scores of Fred and Leona
X1 and X2 are independent.
Since X1 and X2 have a
Now,
For any two variables,
The mean of the difference is equal to the difference of their means.
When the random variables are independent, the variance of the difference is equal to the sum of their variances.
We know that
The standard deviation is the square root of the variance.
Thus,
The difference ( X2 - X1 ) follows a Normal distribution.
Now,
For Probability:
Calculate the z − score,
Or
Use normal probability table in the appendix, to find the corresponding probability.
See the row that starts with -1.7 and the column that starts with .07 of the standard normal probability table for
Thus,
Probability that the scores differ by 5 or more points in either direction is 0.0768.
Chapter 6 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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