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A population that consists of 500 observations has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:

a. 2.50.
b. 12.50.
c. 1.343.
d. 1.50.

Respuesta :

Answer:

The option D) 1.50 is correct

That is the standard error of the sample mean is 1.50

Step-by-step explanation:

Given that a population that consists of 500 observations has a mean of 40 and a standard deviation of 15.

A sample size is 100  taken at random from the given population.

To find the standard error of the sample mean :

From the given Mean=40 and [tex]\sigma =15[/tex]

For N=100

The formula for standard error is [tex]SE_{mean}=\frac{\sigma}{\sqrt{N}}[/tex]

Substitute the values in the above formula we get

[tex]SE_{mean}=\frac{15}{\sqrt{100}}[/tex]

[tex]=\frac{15}{10}[/tex]

[tex]=1.50[/tex]

∴ [tex]SE_{mean}=1.50[/tex]

∴ The standard error of the sample mean is 1.50

Hence the option D) 1.50 is correct

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