Find 'k' (# of standard deviations from the mean)

In summary, the problem involves finding the value of 'k' in the equation P(μ−kσ<X<μ+kσ)≥1− 1/k^2. The person has been able to correctly solve for 'k' in previous problems by taking the absolute value of the portion being looked at, dividing it by two, and then dividing by the standard deviation. However, in this particular problem, the value of 'k' is given as 2.5 instead of the expected (5/4). The person is seeking ideas for solving this discrepancy.
  • #1
rogo0034
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0

Homework Statement


μ=10 σ^2=4

I seem to be getting the first two just time the same as i get every other problem, but I can't seem to get C)'s 'k'. typically i will take the absolute value of the portion that we are looking at, i.e. P(-10<X<10) would be |-10+10| = 20, divide that by two to get the center, 20/2 = 10 and then divide that by the standard deviation, which for this problem is 2. So 10/2 = 5, which i use for K. It's worked for every problem so far, but for C) they have 2.5 instead of (5/4) that i get. Any ideas?

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Homework Equations



P(μ−kσ<X<μ+kσ)≥1− 1/k^2

The Attempt at a Solution

 
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  • #2
A) P(X<10) = P(X≤10) = P(X<μ+kσ) = P(X<10+kσ) = P(μ−kσ<X<μ+kσ) B) P(X>10) = P(X≥10) = P(X>μ+kσ) = P(X>10+kσ) = P(μ−kσ<X<μ+kσ)C) P(−10<X<10) = P(X>−10) & P(X<10) = P(X>μ−kσ) & P(X<μ+kσ) = P(μ−kσ<X<μ+kσ)
 

Related to Find 'k' (# of standard deviations from the mean)

1. What is the purpose of finding 'k' (# of standard deviations from the mean)?

The purpose of finding 'k' is to determine the distance of a data point from the mean in terms of standard deviations. This can help identify outliers or extreme values in a data set.

2. How do you calculate 'k'?

'k' can be calculated by taking the difference between the data point and the mean, and dividing it by the standard deviation of the data set.

3. What does a positive or negative value of 'k' indicate?

A positive value of 'k' indicates that the data point is above the mean, while a negative value indicates that the data point is below the mean.

4. Is 'k' always a whole number?

No, 'k' can be a decimal value as it represents the number of standard deviations from the mean. However, some statistical tests may require 'k' to be a whole number.

5. How can finding 'k' be useful in data analysis?

Finding 'k' can be useful in identifying and understanding the distribution of data. It can also help in making comparisons between different data sets that have different means and standard deviations.

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