The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n=50?
To find the approximate standard deviation of the sampling distribution of the mean for all samples with a sample size of n = 50, we can use the formula:
Standard Deviation of the Sampling Distribution of the Mean (Οπ₯Μ) = Standard Deviation of the Population (Ο) / β(Sample Size)
Given:
Standard Deviation of the Population (Ο) = 21 hours
Sample Size (n) = 50
Plugging the values into the formula:
Οπ₯Μ = 21 / β50
Now, let's calculate the approximate standard deviation of the sampling distribution of the mean:
Οπ₯Μ = 21 / β50
Using a calculator or simplifying further:
Οπ₯Μ β 2.97
Therefore, the approximate standard deviation of the sampling distribution of the mean for all samples with a sample size of n = 50 is approximately 2.97 hours.