In a given normal distribution, the standard deviation is 14.4 and 8.27% of the distribution lies to the left of 60. What is the mean?
see the second applet: Choose parameters and the cut-off points will be calculated. choose a mean of zero, and shaded area .0827, below.
You will be given by that button the standard deviations. So if you know that and the standard deviation, you can multiply to get the mean. http://davidmlane.com/hyperstat/z_table.html
Hey--that is clever!! Thank you.
To find the mean of the given normal distribution, you can use the concept of the z-score.
The z-score is the number of standard deviations away from the mean a particular value is. We can use the z-score formula to find the z-score corresponding to the value 60.
The formula for the z-score is given by:
z = (x - μ) / σ
Where:
z = z-score
x = given value (60 in this case)
μ = mean
σ = standard deviation
Substituting the given values into the formula, we have:
8.27% = (60 - μ) / 14.4
To find the z-score corresponding to 8.27%, we can look it up in the standard normal distribution table or use a statistical software. The z-score corresponds to the cumulative area to the left of the z-score.
Once you have the z-score, you can rearrange the formula to solve for the mean (μ):
(60 - μ) / 14.4 = z
Simplifying the equation:
60 - μ = z * 14.4
Now, substitute the value of z obtained from the z-score table or software and solve for the mean (μ).
Once you find the value of μ, you will have the mean of the given normal distribution.