Question

The mean and the standard deviation of the sampled population​ are, respectively, 77.4 and 4.0. Find the mean and standard deviation of the sampling distribution of the sample mean x overbar for samples of size n equals 225. Round your answers to one decimal place.

Answer 1

See explanation below.

Explanation:

We are looking for the mean and the standard deviation of the sampling distribution of the sample of mean x, given that the mean and standard deviation of sampled population are as follows:

Mean=μ= 77.4

Standard deviation = σ = 4.0

Sample size n = 255

so, the mean of sample mean x will be same as mean of the sampled population:

μₓ = μ = 77.4

and the standard deviation of sample mean x will be standard deviation of the sampled population divided by square root of sample size:

σₓ = σ / √ n

= 4.0 / √225

= 4.0 / 15

= 0.3