Question: If a distribution has a mean of 100 and a standard deviation of 15, what value would be +2 standard deviations from the mean?
How would you go about solving this? Find the z-score of 2? I know that 95% (if i'm not mistaken) covers 2 standard deviations.
If the mean is 100 and the standard deviation is 15, then 2 sd from the mean is 100 + 15 + 15 a mark of ... to the right of the mean and a mark that much to the left of the mean.
The z-score refers to the percent of the data that lies to the left of the mark you are seeking.
Probably the most useful applet for statistics, just enter
mean=100
sd = 15
2 standard deviations would put you at 130
click either above or below after entering 130
http://davidmlane.com/normal.html
Well, well, well, let's dive into the world of statistics! To find the value that is 2 standard deviations above the mean, we can use the z-score formula.
The z-score formula goes like this:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we want to transform into a z-score
- μ is the mean
- σ is the standard deviation
In this case, the mean (μ) is 100, the standard deviation (σ) is 15, and we want to find the value (x) that corresponds to +2 standard deviations above the mean.
So, let's do some quick math!
z = (x - 100) / 15
To find the value that corresponds to a z-score of +2, we can rearrange the equation:
2 = (x - 100) / 15
Now, let's solve for x. Brace yourself, math is coming!
2 * 15 = x - 100
30 = x - 100
x = 130
So, my friend, +2 standard deviations from the mean of 100 is a solid value of 130 in this case! Keep those numbers churning!
To find the value that is +2 standard deviations from the mean, you can use the z-score formula. The z-score is a measure of how many standard deviations an observation is away from the mean.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
z is the z-score,
x is the value you want to find,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
In this case, the mean is 100 and the standard deviation is 15. We want to find the value that is +2 standard deviations from the mean, so we can substitute these values into the formula:
z = (x - 100) / 15
Since we want to find the value that is +2 standard deviations from the mean, we can set z = 2 and solve for x:
2 = (x - 100) / 15
To isolate x, we can multiply both sides of the equation by 15:
2 * 15 = x - 100
30 = x - 100
x = 30 + 100
x = 130
Therefore, the value that is +2 standard deviations from the mean is 130.