Question

If the standard deviation of a random variable X is 20 and a random sample of size nequals19 is​ obtained, what is the standard deviation of the sampling distribution of the sample​ mean?

Answer 1

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

Answer 2

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:

$\sigma_m=\dfrac{\sigma}{\sqrt{n} }$   --- (1)

Now put the value of $\sigma$ that is 20 and the value n that is 19 in the equation (1).

$\sigma_m = \dfrac{20}{\sqrt{19} }$

$\sigma_m = \dfrac{20}{4.36}$

$\sigma_m = 4.587$

So, the standard deviation of the sampling distribution of the sample​ mean is 4.587.

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https://brainly.com/question/2561151