Question

• Using the central limit theorem, what is the distribution of sample means when the population distribution is the following?
• 
  
• 
  
• 
  

• Part (a)

  rectangular

• Part (b)

  normally distributed

• Part (c)

  positively skewed

• Part (d)

  nonmodal

• Part (e)

  multimodal

• Part (f)

  negatively skewed

Answer 1

Central limit theorem:

If a simple random sample of size n is selected from a distribution with mean and standard deviation, then the distribution of the sample mean approach to the normal distribution, as sample size increases.

So there is given any distribution the sample mean follows the normal distribution.

a)

Using central limit theorem the sample mean follows the normal distribution.

b)

Using central limit theorem the sample mean follows the normal distribution.

c)

Using central limit theorem the sample mean follows the normal distribution.

d)

Using central limit theorem the sample mean follows the normal distribution.

e)

Using central limit theorem the sample mean follows the normal distribution.

f)

Using central limit theorem the sample mean follows the normal distribution.