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Answer :
The 99.5% confidence interval for the population mean μ, based on a sample of size 35 with a mean of 36.3 and a standard deviation of 5.1, is (34.580, 38.020) (rounded to one decimal place).
To calculate the 99.5% confidence interval, we need to use the formula:
CI = x ± Z * (σ / √n),
where CI represents the confidence interval, x is the sample mean, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
Given the sample mean x = 36.3, the standard deviation σ = 5.1, and the sample size n = 35, we need to find the Z-score corresponding to a 99.5% confidence level. The Z-score can be obtained from a Z-table or a statistical calculator. Rounded to 3 decimal places, the Z-score for a 99.5% confidence level is approximately 2.807.
Plugging in the values into the formula, we have:
CI = 36.3 ± 2.807 * (5.1 / √35).
Calculating this expression, we find:
CI = (34.580, 38.020).
Therefore, the 99.5% confidence interval for the population mean μ, based on the given sample, is (34.580, 38.020) (rounded to one decimal place). This means that we can be 99.5% confident that the true population mean falls within this interval.
Learn more about standard deviation here:
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