Question

1. If the original population is normally distributed, will random sample means and random sample percentage have distribution that is also normally distributed? Explain.

2. If the original population is skewed, will random sample means and random sample percentage have a distribution that is also normally distributed? If not, what sample size will ensure that the sampling distribution is normal?

3. State the Central Limit Theorem (one of the most important theorems in statistics.)

4. what are some of the consequences of the central limit theorem and how does it relate to the

Answer 1

1) If the population is normally distributed then all the samples taken from it is also normally distributed also the statistics such as mean and percentages is also normally distributed

2) If the population distribution is skewed the sample may or may not follow the population distribution. that depends upon the number of samples taken. Generally a sample size of 30 or more is enough to consider that the sample is normally distributed

3)Central limit theorem: if X1,X2....Xn be the iid the sample taken from any population distribution. if the samples taken are large then the central limit states that ( X - u ) / Sx will follow a normal distribution no matter what is the distribution of the original population.

4) A central limit theorem is one of the most significant theorems in statistics. it simplifies many complex statistics mathematics. Under the assumtipn of normal distrubution most of the test in statistics have been define