For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size- (b) 3.
Take standard deviation and divide it by the square root of the sample size.
a population has a mean of 1100 an st. dev of 15. ind the mean and st.dev of the sample mean with the given size :
a) n- 50
b)n = 50
Well, let me put on my math clown shoes for this one. *twirls around*
To find the standard deviation of the distribution of means for samples of size 3, it's like trying to balance on a unicycle while juggling three balls. It requires a little bit of math circus trickery.
The standard deviation of the distribution of means (also known as the standard error of the mean) is given by the formula:
standard deviation of the distribution of means = standard deviation of the population / square root of the sample size
So, in this case, with a population standard deviation of 10 and a sample size of 3, the formula would be:
standard deviation of the distribution of means = 10 / square root of 3
Now, let me take out my juggling pins and do some calculations. *starts juggling pins*
Calculating... calculating... *pins start falling*
Oh, dear. It seems I dropped a few pins. Let me try that again.
Calculating... calculating... *pins fall again*
I apologize, it seems I'm having trouble with my juggling skills today. Let's just end this circus act quickly.
The standard deviation of the distribution of means for samples of size 3, with a population standard deviation of 10, is approximately 5.773. So, hold on tight to your funny hats and enjoy the statistical rollercoaster!
*drops pins one last time and takes a bow*
To calculate the standard deviation of the distribution of means for samples of size 3, you can use the concept of the standard error of the mean. The formula to calculate the standard error of the mean is:
Standard Error of the Mean = Standard Deviation of the population / Square Root of Sample Size
Since the standard deviation of the population is given as 10, and the sample size is 3, we can plug in these values in the formula:
Standard Error of the Mean = 10 / √3
To get the numerical value, we can calculate the square root of 3:
√3 ≈ 1.732
Now, we can substitute this value into the formula:
Standard Error of the Mean ≈ 10 / 1.732
Calculating this value, we get:
Standard Error of the Mean ≈ 5.774
Therefore, the standard deviation of the distribution of means for samples of size 3 is approximately 5.774.
To calculate the standard deviation of the distribution of means for samples, we need to use the formula for the standard deviation of the sample mean, also known as the standard error of the mean. This formula is:
Standard Error of the Mean (SE) = Standard Deviation (σ) / √Sample Size (n)
In this case, the standard deviation of the population is given as 10, and we want to calculate the standard deviation of the distribution of means for samples of size 3.
Using the formula, we can substitute the values:
SE = σ / √n
where σ = 10 and n = 3.
SE = 10 / √3
Calculating the square root of 3, we get approximately 1.732.
SE ≈ 10 / 1.732
Simplifying the division, we can multiply the numerator and denominator by 1.732:
SE ≈ 5.774
Therefore, the standard deviation of the distribution of means for samples of size 3 from a population with a standard deviation of 10 is approximately 5.774.