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Answer :
The mean (μ) of the population is 97.9 and the standard deviation (σ) is 20. We want to find the standard error of the mean (SE) for a random sample of size n = 233.
The standard error of the mean (SE) is a measure of the variability of the sample means. It tells us how much the sample means are likely to vary from the population mean.
The formula to calculate the standard error of the mean is:
SE = σ / √n
where:
SE is the standard error of the mean
σ is the standard deviation of the population
n is the sample size
In this case, the standard deviation (σ) is 20 and the sample size (n) is 233. Plugging these values into the formula, we get:
SE = 20 / √233
Calculating this value, we find that the standard error of the mean is approximately 1.3042 (rounded to 4 decimal places).
Therefore, the standard error of the mean for a random sample of size n = 233, with a population mean of 97.9 and a standard deviation of 20, is approximately 1.3042.
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