Answer:
a) 5.6 years
b) 0.4478
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 5.6 years
Standard Deviation, σ = 1.9 years
Sample size, n = 18
We are given that the distribution of amounts of time is a bell shaped distribution that is a normal distribution.
a) Mean of each sample.
The best estimator of the sample mean is the population mean itself. Thus, we have:
[tex]\mu_{x} = \mu = 5.6[/tex]
Thus, the sample mean is 5.6 years.
b) Standard error
Formula:
[tex]S.E = \dfrac{\sigma}{\sqrt{n}}[/tex]
Putting values, we have.
[tex]S.E = \dfrac{1.9}{\sqrt{18}} = 0.4478[/tex]
Thus, the standard error is 0.4478.
This question is based on statistics. Therefore, the value of mean is 5.6 years and standard error is 0.4478.
Given:
Mean, μ = 5.6
Standard deviation, σ = 1.9
Samples of size, n = 18
According to the question,
a) Now, calculating the mean of each sample.
Thus,the best estimator of the sample mean is the population mean itself.
[tex]\mu_x = \mu = 5.6[/tex]
Therefore, the sample mean is 5.6 years.
b) Now calculating the standard error,
By using formula,
[tex]Standard \, error = \dfrac{\sigma}{\sqrt{n} }[/tex]
It is given that, standard deviation, σ = 1.9 and samples of size, n = 18,
[tex]Standard \, error = \dfrac{1.9}{\sqrt{18} }= 0.4478[/tex]
Therefore, the value of mean is 5.6 years and standard error is 0.4478.
For further details, prefer this link:
https://brainly.com/question/13179711
