Mean, Variance, and Standard Deviation for the binomial distribution

1
Mean, Variance, and Standard Deviationfor the
binomial distribution

• For a binomial distribution,

2
Example

• Randomly guessing on a 100 question
  multiple-choice test, where each question has 4
  possible answers,

3
Example

• Using our range rule of thumb,

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.
4
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 mean40, stddev4.5. This
  suggests that outcomes of 31 to 49 would be usual
  occurrences. Since 45 falls in that range, we
  shouldnt consider it unusual.

5
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.

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Homework

• 4.4 1, 5, 7, 11, 13