Question

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18

Answer 1

The mean and the standard error of the distribution of the sample mean are 200 and 2.

Explanation:

Consider the provided information.

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18

Sample size = n = 81

Mean = μ=200

Standard deviation = σ = 18

The mean of the distribution of the sample mean is same as the mean of the population.
`\mu_x=\mu=200`

The standard error can be calculated as:
`S.E.=(\sigma)/(√(n))`

Substitute the respective values in the above formula.

`S.E.=(18)/(√(81))=(18)/(9)=2`

Hence, the mean and the standard error of the distribution of the sample mean are 200 and 2.