Question

This is all one question under a post.

• What is the difference between a frequency distribution and a sampling distribution?
• Describe the circumstances under which the Central Limit can/should be applied. For example: imagine you were talking to a classmate who needs help with this topic. How do you know when to use the Central Limit Theorem.
• Describe how to use the Central Limit Theorem. That is, what about using it is the same as previous work you've done? What about it is different?
• In general, what do the symbols μ¯x and σ¯x represent? What are the values of μx¯ and σ¯x for samples of size 110 randomly selected from a population of IQ scores with a population mean of 105 and population standard deviation of 20?
• A typical adult has an average IQ score of 105 with a standard deviation of 20. If 110 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?

Answer 1

>> A frequency distribution is the distribution of its sample data point with respect to the frequency of the data. whereas sampling distribution is the distribution of the sample distribution based upon probability.

>>Circumstances under which we can apply central limit theorem are

-- The data must be randomly drawn from the population

-- The data must be independent

-- The size of the sample must be greater than 30.

>> If you use a central limit theorem then you can assume that the sampling distribution is normally distributed. This makes the maths much easier.

>> μ¯x and σ¯x represent the mean and standard deviation of the sample respectively.

Here  μ¯x = 105

and σ¯x = 20

>>