IQ scores are normally distributed with a mean of 105 and a standard deviation of 18. Assume that many samples of size n are taken form a large population of people and the mean IQ score is computed for each sample. If the sample size is n=64, find the mean and standard deviation of the distribution of sample means.
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To find the mean and standard deviation of the distribution of sample means, we need to use the following formulas:
Mean of the distribution of sample means (µx̄) = Population Mean (µ) = 105
Standard deviation of the distribution of sample means (σx̄) = Population Standard Deviation (σ) / √Sample Size (n)
Given that the population standard deviation (σ) is 18 and the sample size (n) is 64, we can substitute these values into the formula to calculate the standard deviation of the distribution of sample means:
σx̄ = 18 / √64 = 18 / 8 = 2.25
So, the mean (µx̄) of the distribution of sample means is equal to the population mean (µ), which is 105. And the standard deviation (σx̄) of the distribution of sample means is 2.25.