According to Chebyshev's theorem, at least a percentage of either,56%,75%,85%,89% of the measurements lie between 119.3 mmHg and 146.9 mmHg.
I really hate to ask any question of you guys I know you are busy, but I am totally lost with this statistic stuff. a little note I failed this course once, and have to take it again in order to get my degree.
Thank you so very much. If someone could just explain in which direction I go I think I can handle it from there.
first question: Do you know what the theorem states?
Chebyshev's theorem is a statistical concept that provides a lower bound on the percentage of measurements that fall within a certain number of standard deviations from the mean in any distribution, regardless of its shape.
In this case, we are given that between 56%, 75%, 85%, or 89% of the measurements lie between 119.3 mmHg and 146.9 mmHg. To understand this, we can use Chebyshev's theorem formula:
P(at least k standard deviations from the mean) >= 1 - 1/k^2
Here, "k" represents the number of standard deviations from the mean, and P represents the percentage of measurements within that range.
To find the answer, we need to determine the value of k.
Let's start with the first option, 56%. We want to find the minimum number of standard deviations that capture at least 56% of the measurements.
Using the formula:
1 - 1/k^2 = 0.56
Solving for k, we have:
1/k^2 = 0.44
k^2 = 1/0.44
k^2 = 2.27
k ≈ 1.51
So, for at least 56% of the measurements to fall between 119.3 mmHg and 146.9 mmHg, you need to consider a range of approximately 1.51 standard deviations from the mean.
You can repeat this process for each percentage provided (75%, 85%, and 89%), plugging in the corresponding value into the equation and solving for k.
Hope this helps you understand the concept of Chebyshev's theorem and how to apply it!