you have helped me so much, one more problem.
Consider the following questions.
(a) Chebychev's theorem guarantees that what percentage of a distribution will be included between x − 2.3s and x + 2.3s. (Give your answer correct to one decimal place.)
Incorrect: Your answer is incorrect. . % I got 75%
(b) Chebychev's theorem guarantees that what percentage of a distribution will be included between x − 3.3s and x + 3.3s. (Give your answer correct to one decimal place.)
I got 89% and both answers are wrong, cant figure it out, have one more try on homework for this one. HELP need this to get a passing score...
a) 1-1/k^2
1- 1/(2.3)^2
1- 1/5.29
(5.29-1)/5.29
= 4.29/5.29
= 81.1%
b) a) 1-1/k^2
1- 1/(3.3)^2
1- 1/10.89
(10.89-1)/10.89
= 9.89/10.89
= 90.8%
To find the percentage of a distribution included between a certain number of standard deviations from the mean, you can use Chebyshev's theorem. Chebyshev's theorem states that for any given data set, at least (1 - 1/k^2) of the data will fall within k standard deviations of the mean, where k is a positive integer greater than 1.
In this case, for part (a), you were given x − 2.3s and x + 2.3s. So, you are looking for the percentage of the data that falls within 2.3 standard deviations from the mean. Using Chebyshev's theorem, we can calculate:
k = 2.3
Percentage included = (1 - 1/k^2) * 100
Plugging in the values:
Percentage included = (1 - 1/2.3^2) * 100
Percentage included ≈ 87.0% (rounded to one decimal place)
Therefore, 87.0% of the distribution is guaranteed to be included between x − 2.3s and x + 2.3s.
For part (b), you need to find the percentage of the data that falls within x − 3.3s and x + 3.3s. Using the same formula:
k = 3.3
Percentage included = (1 - 1/k^2) * 100
Plugging in the values:
Percentage included = (1 - 1/3.3^2) * 100
Percentage included ≈ 91.4% (rounded to one decimal place)
Therefore, 91.4% of the distribution is guaranteed to be included between x − 3.3s and x + 3.3s.
I hope this explanation helps you understand how to calculate the percentages using Chebyshev's theorem. Good luck with your homework!