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Answer:
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 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:
As the sample size is large, i.e. <em>n</em> = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of as follows:
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.