
To find:
The

Answer to Problem 30E
Solution:
The probability that out of 350 entering college freshmen, 100 will need to take developmental mathematics is
Explanation of Solution
Given:
Total number of independent trials is 350.
Probability of an individual trial success is
Concept:
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 subtracting and adding
Thereafter, the
Following which, area under curve is computed by using a z-table.
Calculation:
Probability of a trial to be success:
Probability of a trial to be failure:
Then mean is:
Also, standard deviation is:
Since here is exact “100”, continuity correction gives
This gives the
Now, the required probability is:
Conclusion:
The probability that out of 350 entering college freshmen, 100 will need to take developmental mathematics is
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Chapter 6 Solutions
Beginning Statistics, 2nd Edition
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