An unknown distribution has a mean of 90 and a standard deviation of 10. Sample size n=36 are drawn randomly from the population. What is the value that is 3 standard deviations above the mean of the sampling distribution
The value that is 3 standard deviations above the mean of the sampling distribution can be found using the formula:
Value = mean + (standard deviation * number of standard deviations)
In this case, the mean of the sampling distribution is equal to the mean of the population, which is 90. The standard deviation of the sampling distribution can be calculated by dividing the standard deviation of the population by the square root of the sample size:
Standard deviation of the sampling distribution = standard deviation of the population / square root of sample size
Substituting the given values:
Standard deviation of the sampling distribution = 10 / √36 = 10 / 6 = 1.6667
To find the value that is 3 standard deviations above the mean of the sampling distribution:
Value = 90 + (1.6667 * 3) = 90 + 5 = 95
Therefore, the value that is 3 standard deviations above the mean of the sampling distribution is 95.