Concept explainers
85th percentile of Djokovic’s first − serve speeds.
Answer to Problem 64E
85th percentile is 117.2 mph.
Explanation of Solution
Given information:
Mean speed,
Standard deviation,
Calculations:
The data value represented by the xth percentile has x% of the data values below it.
That implies
The data value represented by the 85th percentile has 85% of the data values below it.
Now,
Find the z − score corresponding the probability of 85% (or 0.85) in the normal probability table of the appendix.
Note that
The closest probability would be 0.8508 that lies in the row 1.0 and in the column .04 of the normal probability table.
Then
The corresponding z − score,
In order to find xth percentile, calculate the z − score
Equate the above two expressions:
Multiply both sides by 5:
Add 112 to both sides:
That becomes
Thus,
85thpercentile will be 117.2 mph.
Chapter 2 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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