Respuesta :
Answer:
The sampling distribution of sample mean is N (112, 4.56).
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the sampling distribution of the sample means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bat x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
In this case, a sample of n = 30 college-educated adults were selected from a large population and their IQ levels were recorded.
The mean IQ level was, μ = 113.
The standard deviation of IQ was, σ = 25.
Since the sample size is large, i.e. n ≥ 30, then according to the Central limit theorem the sampling distribution of sample mean can be approximated by the Normal distribution.
The mean of the sampling distribution of sample mean is:
[tex]\mu_{\bat x}=\mu=112[/tex]
The standard deviation of the sampling distribution of sample mean is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{30}}=4.56[/tex]
Thus, the sampling distribution of sample mean is N (112, 4.56).
