An unknown distribution has a mean of 90 and a standard deviation of 16. Sample size n=64 are drawn randomly from the population. What is the value that is 3 standard deviations above the mean of the sampling distribution
The standard deviation of the sampling distribution can be calculated using the formula:
Standard Deviation (sampling distribution) = Standard Deviation (population) / √(sample size)
In this case, the standard deviation of the population is 16 and the sample size is 64. Plugging these values into the formula:
Standard Deviation (sampling distribution) = 16 / √(64) = 16 / 8 = 2
To find the value that is 3 standard deviations above the mean of the sampling distribution, multiply the standard deviation by 3 and add it to the mean:
Value = (Standard Deviation (sampling distribution) * 3) + Mean
Value = (2 * 3) + 90 = 6 + 90 = 96
Therefore, the value that is 3 standard deviations above the mean of the sampling distribution is 96.