How do I find the value of the mean, when I am only given the std dev of a normal distribution and a percentage of values greater than another value.
Use the same formula you have to find the z-score
I don't know if you use tables from the back of a textbook, or some webpage like David Lane's fabulous page
http://davidmlane.com/hyperstat/z_table.html
suppose that the percentage of Alice getting a mark of 75 or less is .62
If the SD is 6 marks what is the mean of the class.
(75 - mean)/6 = .62
75 - mean = 3.72
mean = 75 - 3.72 = appr 71.3
To find the value of the mean of a normal distribution when you are given the standard deviation and a percentage of values greater than another value, you need to follow a two-step process:
Step 1: Find the z-score
The z-score measures the number of standard deviations a particular value is away from the mean. To find the z-score for the given percentage, you can use a standard normal distribution table or a calculator:
1. Subtract the given percentage from 100 to obtain the percentage below the value.
2. Convert the percentage to a decimal.
3. Use the z-score table or calculator to find the corresponding z-score.
Step 2: Use the z-score to find the mean
Once you have the z-score, you can use the formula for z-score:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value you want to find the mean for
- μ is the unknown mean
- σ is the given standard deviation
Rearrange the formula to solve for μ:
μ = x - (z * σ)
Substitute the known values to find the mean (μ).
Note that in a normal distribution, the mean is also the median and the mode, so finding the mean provides an estimate for these values as well.