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The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.
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:
µ = p
The standard deviation of this sampling distribution of sample proportion is:
σ = √p(1-p)/n
The information provided is:
p = 0.14
n = 41
As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.
Compute the values of P(p^ - p >0.04) as follows:
P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411
= P(Z>2.33)
= 0.990
Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990
Learn more about Normal distribution here:
brainly.com/question/25638875
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