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 (σ𝑥̄) = Standard Deviation of the Population (σ) / √(Sample Size)
Given:
Standard Deviation of the Population (σ) = 21 hours
Sample Size (n) = 50
Plugging the values into the formula:
σ𝑥̄ = 21 / √50
Now, let's calculate the approximate standard deviation of the sampling distribution of the mean:
σ𝑥̄ = 21 / √50
Using a calculator or simplifying further:
σ𝑥̄ ≈ 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.