A population of values his normal distribution with men equal to 27.6 and standard deviation equal 39.4 do you intend to draw a

Question

3 years ago

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random sample of size N equal 173 what is the mean of the distribution of sample means

1 answer:

Alecsey [184] · Answer 1 · 2022-01-19T18:55:37+03:00

Answer:

The mean of the distribution of sample means is 27.6

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 27.6

Standard Deviation, σ = 39.4

We are given that the population is a bell shaped distribution that is a normal distribution.

Sample size, n = 173.

We have to find the mean of the distribution of sample means.

Central Limit theorem:

It states that the distribution of the sample means approximate the normal distribution as the sample size increases.
The mean of all samples from the same population will be approximately equal to the mean of the population.

Thus, we can write:

$\mu_{\bar{x}} = \mu = 27.6$

Thus, the mean of the distribution of sample means is 27.6