Transcript Mean, Variance, and Standard Deviation for the binomial

Mean, Variance, and Standard Deviation
for the binomial distribution
For a binomial distribution,
  n p
  n pq
2
  n pq
Example
Randomly guessing on a 100 question
multiple-choice test, where each question
has 4 possible answers,
  100 1 4  25
 2  100 1 4  3 4  18.8
  100 1 4  3 4  4.3
Example
Using our range rule of thumb,
  2  25  2  4.3  16.4
  2  25  2  4.3  33.6
It would be unusual to get less than 17 questions
correct, or more than 33 question correct if you were
randomly guessing on the test.
Another Example
You presume that people are evenly split (50/50) on
their preference between two candidates. You poll
80 people, and find 45 prefer candidate A. Is this
unexpected?
We could find P(45 or more).
Alternatively, using our presumed 50/50 preference,
find mean=40, stddev=4.5. This suggests that
outcomes of 31 to 49 would be usual occurrences.
Since 45 falls in that range, we shouldn’t consider
it unusual.
Another Example
Now suppose you poll 800 people, and 450
prefer candidate A. Is this unexpected?
Using our presumed 50/50 preference, mean =
400, stddev = 14.1. Again using the range
rule of thumb, this suggests that outcomes
of 372 to 428 would be usual.
Since the outcome of 450 is unusual, we
should question whether our presumption of
a 50/50 split is accurate.
Homework
4.4: 1, 5, 7, 11, 13