Question

Suppose the population of IQ scores in the town or city where you live is bell-shaped, with a mean of 104 and a standard deviation of 35. Describe the frequency curve for possible sample means that would result from random samples of 100 IQ scores.

Answer 1

Answer:

The mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.  

Step-by-step explanation:

We know the population mean and standard deviation, that has a bell-shaped distribution:

$\mu=104\\\\\sigma=35$

The sampling distribution, the distribution of the mean of samples of size n out of this population, will have the same mean as the population mean.

$\mu_M=\mu=104$

The standard deviation will be related to the population standard deviation and the sample size as:

$\sigma_M=\frac{\sigma}{\sqrt{N}} =\frac{35}{\sqrt{100}}=3.5$

Then, the mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.