How large a sample from N(80,20) population is needed so that the sampling distribution of the mean has a standard deviation of 1?
To determine the sample size needed for the sampling distribution of the mean to have a standard deviation of 1, we can use the formula for the sampling distribution of the mean:
Standard Deviation of the Sampling Distribution of the Mean (σx) = Standard Deviation of the Population (σ) / √(Sample Size)
Given that the population has a mean of 80 and a standard deviation of 20 (N(80,20)), and we want the standard deviation of the sampling distribution of the mean (σx) to be 1, we can rewrite the formula as:
1 = 20 / √(Sample Size)
To solve for the sample size, we rearrange the equation:
√(Sample Size) = 20 / 1
Sample Size = (20 / 1)^2
Sample Size = 20^2
Sample Size = 400
Therefore, a sample size of 400 is needed from the population N(80,20) so that the sampling distribution of the mean has a standard deviation of 1.