Respuesta :
Answer:
σ m = 4.56 (approx.)
Step-by-step explanation:
Standard deviation of the sampling distribution of the sample mean [σ m] : is a measure of Sample dispersion. It is also called standard error. It falls with increase in sample size
Standard Deviation of sample mean [σ m] = σ / √ n
Given : Standard Deviation = σ = 20
Number of sample units : n = 19
[σ m] = 20 / √ 19
= 20 / 4.36
= 4.56
The standard deviation of the sampling distribution of the sample mean is 4.587 and this can be determined by using the formula of the standard deviation of the sample mean.
Given :
The standard deviation of a random variable X is 20 and a random sample of size n equals 19.
The formula of the standard deviation of the sample mean can be used to determine the standard deviation of the sampling distribution of the sample mean.
The standard deviation of the sample mean is given by:
[tex]\sigma_m=\dfrac{\sigma}{\sqrt{n} }[/tex] --- (1)
Now put the value of [tex]\sigma[/tex] that is 20 and the value n that is 19 in the equation (1).
[tex]\sigma_m = \dfrac{20}{\sqrt{19} }[/tex]
[tex]\sigma_m = \dfrac{20}{4.36}[/tex]
[tex]\sigma_m = 4.587[/tex]
So, the standard deviation of the sampling distribution of the sample mean is 4.587.
For more information, refer to the link given below:
https://brainly.com/question/2561151
