Arandom variable is normally distributed. it has a mean of 245 and a standard deviation of 21. a.) for a sample of size 10, state the mean of the sample mean. b.) for a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean"). c.) for a sample of size 35, state the mean of the sample mean. d.) for a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean"). e.) true or false: as sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases.

a) By the Central Limit Theorem, 245

b) 6.64

c) By the Central Limit Theorem, 245

d) 3.55

e) False

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

a.) for a sample of size 10, state the mean of the sample mean.

By the Central Limit Theorem, 245

b.) for a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean").

c.) for a sample of size 35, state the mean of the sample mean.

By the Central Limit Theorem, 245

d.) for a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean").

e.) true or false: as sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases.

The standard error of the mean is given by . So, as n(sample size) increases, s(standard deviation of the sample mean) decreases. So this is false.