If X is a normal random variable with a mean of 20 and standard deviation of 2,

Question

If X is a normal random variable with a mean of 20 and standard deviation of 2, which of the following could be the graph of the distribution of X?

Which of the following statements explains the following graphic, which includes a picture of a distribution along with three sampling distributions of the mean with different sample sizes:

Averages calculated from larger samples will be less variable.

Averages calculated from larger samples will be more variable.

Averages calculated from larger samples will be larger.

Averages calculated from larger samples will be closer to zero

Averages calculated from larger samples will be less variable.

Averages calculated from larger samples will be more variable.

Averages calculated from larger samples will be larger.

Averages calculated from larger samples will be closer to zero

Explanation / Answer

A) THE CORRECT REPRESENTATION OF THE MEAN AND THE STANDARD DEVIATION GRAPH WILL BE IN THE OPTION D AS IN ONLY GRAPH D THE GRAPH IS POINTED TOWARDS THE MEAN AND ALSO THE PEAL IS CLOSE TO 0.2

HENCE THE OPTION D IS CORRECT.

B) AS WE KNOW THAT THE VARIANCE IS ALWAYS INVERSELY PROPORTION TO THE SIZE OF N AND HENCE THE SIZE INCREASES THE VALUE OF VARAINCE REDUCES

THEREFORE THE CORRECT REPRESENTATION OF THE GRAPH WILL BE THE MORE THE SIZE OF THE SAMPLE THE AVERAGE IS LESS VARIABLE.

THEREFORE OPTION A is correct.

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