Answer:
Explanation:
Use the mean and the standard deviation obtained from the last discussion and test the claim that the mean age of all books in the library is greater than 2005.
This is the last discussion:
The science portion of my library has roughly 400 books.
They are arranged, on shelves, in order of their Library of Congress
code and, within equal codes, by alphabetical order of author.
Sections Q and QA have a total of 108 books.
The bulk of the library was established in the early 1990s.
I used a deck of cards, removing the jokers and face cards, keeping
only aces (1) and "non-paints" (2 to 10). Starting from the start of
the first shelf, I would turn a card (revealing its number N) and I
would go to the Nth book. This uses ordinal numbers (1 would means the
"first" book, not a gap of 1).
The cards were shuffled sufficiently to assume that the cards have a
random order.
I sampled only the LC subsections Q and QA (therefore, not a true
sample of the entire library, as this classification is not purely
random).
Thus, I picked 21 books (the expected number being 108/5.5 = 19.6 --> 20 books)
The sampled dates of publication were (presented as an ordered set):
1967, 1968, 1969, 1975, 1979, 1983, 1984,
1984, 1985, 1989, 1990, 1990, 1991, 1991,
1991, 1991, 1992, 1992, 1992, 1997, 1999
The median date is 1990
The mean date is 1985.67
Variance = 84.93 ( Sum of (date-mean)^2 )
SQRT of variance = 9.2 (sample standard deviation)
The "sigma-one" confidence interval (containing 68% of the books), if
the sample were NOT skewed, and if the distribution were "normal"
would contain dates from "mean - 9.2" to "mean + 9.2"
Sigma-2 (95%) would have mean - 2(9.2) to mean + 2(9.2)
Sigma-3(99.7%) from "1985.67 - 3(9.2)" to "1985.67 + 3(9.2)"
1958.07 to 2012.6
There, you see one reason why the distribution is skewed (it is
possible to have books older than 1958, but it is impossible to have
book newer than 2012), but it still represents a usable model for the
library. If it applies to the entire library of 400 books, you would
expect one book (0.3% of 400) to fall outside the 3-sigma interval.