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?

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

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