Answer:
Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ=11.6. Assume the population is normally distributed.
To determine the minimum sample size required to be 99% confident that the sample mean is within one unit of the population mean with a standard deviation of 11.6 and assuming the population is normally distributed , we can use the following formula:
n = (z*σ / E)^2
where n is the sample size, z* is the z-score corresponding to the confidence level (in this case, 2.58 for 99% confidence), σ is the population standard deviation, and E is the maximum error or distance between the sample mean and the population mean (in this case, 1 unit).
Plugging in the given values, we get:
n = (2.58 * 11.6 / 1)^2 n ≈ 284.7
Rounding up to the nearest whole number, we get a minimum sample size of 285. Therefore, we need a sample size of at least 285 to be 99% confident that the sample mean is within one unit of the population mean , assuming a normal population distribution and a population standard deviation of 11.6.
Explanation: