d. Using the Empirical Rule, what percentage of household credit card debt is mo

Question

d. Using the Empirical Rule, what percentage of household credit card debt is more than 3 standard deviations above the mean? What is the dollar value? Percentage of the distribution Dollar value at three standard deviation above the mean 3. General Concepts a. The Central Limit Theorem says that for large enough samples, if you take repeated samples from a skewed distribution: (choose one) the means of the samples will have a uniform distribution. the means of the samples will have a skewed distribution. the means of the samples will have a bimodal distribution. the means of the samples will have the same shape distribution as the original data. the means of the samples will have a normal or approximately normal distribution. b. What does the z-score represent? Use the Empirical Rule to find the approximate probabilities below. Assume that you are working with a Normal distribution. 4. Approximately what percentage of a normal distribution falls between the one and two standard deviations above the mean? means "approximately") ~0.15% a. "2.35% "34% ~13.5% ~47.5% _ Approximately what percentage of a normal distribution falls between two standard deviations +2a) above the mean and three standard deviations +3a) above the mean? b. 49.85 -2.35% -0.15% -47.5%

Explanation / Answer

Approximately 99.7% of the data falls within three standard deviations of the mean (or between the mean – three times the standard deviation and the mean + three times the standard deviation). The following notation is used to represent this fact: ± 3,

so calculation of above the ± 3=100 -99.7= 0.3%

pecentage area under the cuve= 100%

General Concept:

-the means of the samples will have a normal or approximately normal distribution.

this is the main use of the central limit theorm when more than 30 samlpe the distribution is converges to normal dstribution.

b) what does the Z-score represent?

-- a z-score is the number of standard deviations from the mean a data point is.

4) Use the empirical rule to find the approximate probabilities below, assme that you are working with normal distribution.

a) approximately what percentage of a normal distribution falls between the one and two standard deviations above the mean?

- 13.5

Because the 1sd=68 and 2sd=95 so difference is =27 so 27/2=13.5

Because 99.7 – 95= 4.7 so 4.7-= 2.35

C what is the probability of a normal distribution have a measurement beyond three standard deviation below the mean?

---- 0.15%

Because the similarly as like the above 0.30/2=0.15

d—the distribution is unimodal and symmetric around the mean.

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