Question

Random sample size of 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. the mean and the standard error of the mean are?

Answer 1

Answer:

the  mean and standard error of the mean are 200 and 2 respectively.

Step-by-step explanation:

Given that ;

the sample size n = 81

population mean μ = 200

standard deviation of the infinite population σ = 18

A population  is the whole set of values, or individuals you are interested in, from an experimental study.

The value of population characteristics such as the  Population mean (μ), standard deviation (σ) are said to be known as the population distribution.

From the given information above;

The sample size is large and hence based on the central limit theorem the mean of all the means is same as the population mean 200.

i.e

$\mu = \bar \mu_x$ = 200

∴ The mean = 200

and the standard error of the mean can be determined via the relation:

$\mathbf{standard \ error \ of \ mean = \dfrac{\sigma}{\sqrt {n}}}$

$\mathbf{standard \ error \ of \ mean = \dfrac{18}{\sqrt {81}}}$

$\mathbf{standard \ error \ of \ mean = \dfrac{18}{9}}$

$\mathbf{standard \ error \ of \ mean =2}$

Therefore ; the  mean and standard error of the mean are 200 and 2 respectively.