(a)
To find: the value of the mean diameter of the large cups.
(a)
Answer to Problem 58E
The mean lid diameter should be 4.00 inches
Explanation of Solution
Given:
The standard deviation remains at
Calculation:
If the standard deviation is 0.2 inches, then it is supposed to find the value of mean diameter that a supplier must set for the large-cup lids to ensure that less than 1% of the lids are too small to fit.
Solve for the appropriate mean so that less than 1% of lids have diameter less than 3.95. First, find the z -value for which 1% of observations are lower. Using standard normal table, find the z value corresponding to
Since this z -value should correspond to a diameter of 3.95,
So the mean lid diameter should be 4.00 inches to ensure that less than 1% of the lids are too small to fit.
Conclusion:
Therefore, the mean lid diameter should be 4.00 inches
(b)
To find: the value of the standard deviation of the lids which are very small to fit.
(b)
Answer to Problem 58E
It is extremely rare for a lid to be too big.
Explanation of Solution
Given:
The mean diameter stays at
Calculation:
If the mean diameter stays at 3.98, then find the value of mean diameter that a supplier must set for the large-cup lids to ensure that less than 1% of the lids are too small to fit.
Solve for the appropriate standard deviation so that less than 1% of lids have diameter less than 3.95. First, find the z -value for which 1% of observations are lower. Using standard normal table, find the z value corresponding to
Hence, the proportion of observations less than 3.5 is approximately 1, so the proportion of observations greater than 3.5 is approximately 0. In other words, it is extremely rare for a lid to be too big.
Conclusion:
Therefore, it is extremely rare for a lid to be too big.
(c)
To find: whether option a or b is preferable.
(c)
Answer to Problem 58E
Part (b) is preferred.
Explanation of Solution
Given:
The mean diameter stays at
Calculation:
Reducing the standard deviation is preferred. This will not increase the number of lids that are too big, but will reduce the number of lids that are too small. If the mean is shifted to the right, reduce the number of lids that are too small, but increase the number of lids that are too big.
Conclusion:
Therefore, part (b) is preferred.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Introductory Statistics
Statistics: The Art and Science of Learning from Data (4th Edition)
Statistical Reasoning for Everyday Life (5th Edition)
Essentials of Statistics, Books a la Carte Edition (5th Edition)
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