Answer:
The correct option is (c) 20 and 2.5.
Step-by-step explanation:
The sample size is, n = 36.
The sample mean is, [tex]\mu=20[/tex]
The sample standard deviation is, [tex]\sigma_{x}=15[/tex]
According to the Central limit theorem, if a random sample of size ≥ 30 is selected from an unknown population, then the sampling distribution of the sample means ([tex]\bar x[/tex]) follows a Normal distribution with mean [tex]\mu_{\bar x}[/tex] and standard deviation [tex]\sigma_{\bar x}[/tex].
The mean is, [tex]\mu_{\bar x}=\mu =20[/tex]
The standard deviation of the sampling distribution of the sample means is known as standard error.
The standard error is:
[tex]\sigma_{\bar x}=\frac{\sigma_{x}}{\sqrt{n} } =\frac{15}{\sqrt{36} }= 2.5[/tex]
Thus, the mean is 20 and the standard error is 2.5.
