# Thread: Normal and skewed Distributions

1. ## Normal and skewed Distributions

6. Womens heights have an approximate normal distribution with mean 64.5 inches and SD 2.5 inches (SAY). Family income is a highly skewed distribution with mean 78,000 dollars and SD 16,500 dollars (SAY). Consider the following averages.
a. The average of 5 randomly selected womens heights
b. The average of 10 randomly selected family incomes
c. The average of 20 randomly selected family incomes
Which of these averages is closest to a normal distribution, and which is least like a normal distribution? Why?

2. Originally Posted by ShaunW 6. Womens heights have an approximate normal distribution with mean 64.5 inches and SD 2.5 inches (SAY). Family income is a highly skewed distribution with mean 78,000 dollars and SD 16,500 dollars (SAY). Consider the following averages.
a. The average of 5 randomly selected womens heights
b. The average of 10 randomly selected family incomes
c. The average of 20 randomly selected family incomes
Which of these averages is closest to a normal distribution, and which is least like a normal distribution? Why?
The average of something normally distributed is also normally distributed (with the sam mean but a SD scalled by a factor of one over the square root of the sample size)

The distribution of the mean of something with an arbitary distribution (subject to some restrictions that we will not discuss here) tends to normallity as the sample size increases, So the bigger the sample size the more normal the mean of a sample from a non-normally distributed RV.

CB

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