The document discusses the mean, variance, and standard deviation of binomial distributions. It provides examples of calculating these values for randomly guessing answers on a multiple choice test and polling voters with a presumed even split between two candidates. It concludes with homework problems involving binomial distributions.

1. Top School in Ghaziabad
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2. Mean, Variance, and Standard Deviation
for the binomial distribution
For a binomial distribution,
n p
 
n p q
  
n p q
2
  



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3. Example
Randomly guessing on a 100 question multiple-choice
test, where each question has 4 possible
answers,
4.3
  
   
4
3
4
100 1
18.8
4
3
4
100 1
25
4
100 1

2
   


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4. 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.
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5. 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.
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6. 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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7. Homework
4.4: 1, 5, 7, 11, 13
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