To find:
The
Answer to Problem 16E
Solution:
The probability that more than 100 out of 300 elections will contain fraud voters is
Explanation of Solution
Given:
Total number of election is 300.
Probability of an individual fraud is
Continuity correction factor approximates discrete distributions to continuous ones by converting a random variable value of the former to a
Binomial distribution is discrete and the probability of
with mean
Normal distribution is continuous and probability of obtaining the value
with mean 0 and standard deviation 1.
The continuity correction is done by changing the whole number
and then the probability
where
In this question, discrete binomial distribution is approximated using the normal distribution, which is continuous.
Initially, the values of
Also, continuity correction is done, according to requirements of the question, that is by adding
Thereafter, the
following which, area under curve is computed by subtracting corresponding value at the standard normal table from one.
Calculation:
which gets converted to:
Then mean is:
Also, standard deviation is:
Since the inequality is “more than”, continuity correction gives
This gives the
Now, the required probability is:
The latter of which is obtained by taking the table values at
Since the
Conclusion:
The probability that more than 100 out of 300 elections will contain fraud voters is
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Chapter 6 Solutions
Beginning Statistics, 2nd Edition
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