Say that you have a population and you measure the number of

Say that you have a population and you measure the number of children in each family. Since the number of children in a family is a \"counting variable\", the population distribution is positively skewed. The population mean number of children in a family is 2.02 and the population standard deviation is 1.94.
What does the Central Limit Theorem tell us about the distribution of sample means from this population when the sample size is 46?

1-- True False  The distribution of sample means will approximate a normal distribution.
2-- True False  The typical distance between the sample means and the population mean is 0.286.
3-- True False  The mean of the distribution of sample means will be 2.02.
4-- True False  The standard deviation of the distribution of sample means will equal 1.94.

Solution

1) The distribution of sample means will approximate a normal distribution. is true.

As sample size increases the means of all samples tend to follow a normal distribution.

2) The typical distance between the sample means and the population mean is 0.286. True. This can take any value.

3) The mean of the distribution of sample means will be 2.02.False It will be 1.94

4) The standard deviation of the distribution of sample means will equal 1.94.(it is 1.94/rtn) Hence false.