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Answer :
The 99% confidence interval for the population mean is (33.49, 36.51), so the answer is A. 30.5 to 38.1.
We can use the formula for the confidence interval for the population mean when the population standard deviation is known:
CI = X ± z*(σ/√n)
where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.
First, let's calculate the z-score for a 99% confidence level. From a standard normal distribution table, we find that the z-score for a 99% confidence level is approximately 2.576.
Next, we can plug in the given values and solve for the confidence interval:
CI = 35 ± 2.576*(5.8/√258)
CI = 35 ± 1.51
CI = (33.49, 36.51)
Therefore, the 99% confidence interval for the population mean is (33.49, 36.51), so the answer is A. 30.5 to 38.1.
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