Respuesta :
Answer:
a) X that is a distribution of number of years of education for self-employed individuals.
b) Mean = 15.1, Standard Deviation = 0.8
c) Mean = 15.1, Standard Deviation = 0.4
Step-by-step explanation:
We are given the following in the question:
The population distribution of number of years of education for self-employed individuals in a certain region has a mean of 15.1 and a standard deviation of 4.8
a) The random variable is X that is a distribution of number of years of education for self-employed individuals.
b) According to central limit theorem, as the sample size increases the distribution of means approaches a normal distribution.
Thus, [tex]\bar{x}[/tex] has a normal distribution with
[tex]\text{Mean} = 15.1\\\text{Srtandard Deviation} = \displaystyle\frac{\sigma}{\sqrt{36}} = \frac{4.8}{\sqrt{36}} = 0.8[/tex]
c) n = 144
[tex]\bar{x}[/tex] has a normal distribution with
[tex]\text{Mean} = 15.1\\\text{Srtandard Deviation} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{4.8}{\sqrt{144}} = 0.4[/tex]
By increasing n, the standard deviation for distribution of mean reduced by one half. Therefore, we see that quadrupling the sample size will reduce the standard deviation by one half.
