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Answer:
The probability that in a random sample of 100 CSU graduates the error is within 5% of the population proportion of 60% is 0.6923.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
The information provided is:
<em>p</em> = 0.60
<em>n</em> = 100
As <em>n</em> = 100 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportions.
The distribution of sample proportion is .
Compute the probability that in a random sample of 100 CSU graduates the error is within 5% of the population proportion of 60% as follows:
Thus, the probability that in a random sample of 100 CSU graduates the error is within 5% of the population proportion of 60% is 0.6923.