Homework Help: statistics

Posted by sophia on Thursday, October 25, 2007 at 8:11pm.

Given a distribution with mean X and standard deviation S, answer the following.

4.1 Determine the mean and standard deviation if constant K is added to each observation
4.2 Determine the mean and standard deviation if constant K is multiplied by each observation
4.3 Assuming no knowledge about the distribution, estimate the percentage of observations that lie within two (2) standard deviations of the mean; explain your approach
4.4 Assuming the distribution is normally distributed, estimate the percentage of observations that lie within two (2) standard deviations of the mean; explain your approach

statistics - MathGuru, Friday, October 26, 2007 at 2:22pm
I'll explain 2 of these questions; see if you can figure out the other two.

4.1 The mean will be changed and the standard deviation will remain the same. There will be no change in standard deviation since each score and also the mean increase by constant K.

4.3 You can use Chebyshev's theorem for any distribution. This theorem says that within 2 standard deviations of the mean, you will always find at least 75% of the data.
There is a formula to show this:
1 - (1/k^2)
If k = 2 (representing 2 standard deviations), then 1 - (1/2^2) = 1 - 1/4 = 3/4 = .75 or 75%.

For 4.2: Calculate mean and standard deviation using an example data set, then multiply each observation in the data set by a constant. See what happens to the mean and standard deviation.

For 4.4: Use the 68-95-99.7 rule which is also called the Empirical Rule.

I hope this will help.

Answer this Question

Related Questions

Statistics - 1) A Motor Company has purchased steel parts from a supplier for ...
Math (Statistic) - Considered the sampling distribution of a sample mean ...
MATH - Which of the following normal distributions has the smallest spread? A. A...
Stastics - When we convert x-value to z- score and use Standard Normal ...
statistics - An SRS of size n is taken from a large population whose ...
statistics - what are the mean and standard deviation of a sampling distribution...
Statistics - data from sample of 400 cases, variable has 95% confidence interval...
statistics/mean and standard deviation - find the mean and standard deviation in...
Statistics - Given that x is a normally distributed random variable with a mean ...
Statistics - 1) Find the missing parameter 1.mean 15, 30.15 %, above 50; what is...

For Further Reading

First Name:
School Subject:
Answer: