Concept explainers
(a)
60th percentile of the first − class letter weights.
(a)
Answer to Problem 68E
60th percentile is 0.73 ounces.
Explanation of Solution
Given information:
Mean,
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 60th percentile has 60% of the data values below it.
Now,
Find the z − score corresponding the
Note that
The closest probability would be 0.5987 that lies in the row 0.2 and in the column .05 of the normal probability table.
Then
The corresponding z − score,
In order to find xthpercentile, calculate the z − score
Equate the above two expressions:
Multiply both sides by 0.16:
Add 0.69 to both sides:
That becomes
Thus,
60thpercentile will be 0.73 ounces.
(b)
Proportion of first − class letters at this post office that require extra postage.
(b)
Answer to Problem 68E
Around 0.0262 of the first − class letters at this post office require extra postage.
Explanation of Solution
Given information:
Weight,
Mean,
Standard deviation,
Calculations:
Calculate the Z − score,
Use normal probability table in the appendix, to find the corresponding probability.
See the row that starts with 1.9 and the column that starts with .04 of the standard normal probability table for
Therefore,
Around 0.0262 of the first − class letters at this post office require extra postage.
Chapter 2 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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