Finding the Standard Deviation from Probability

[Samwise_geegee]

Homework Statement

For a certain random variable X, P(X≤500)=.5 and P(X>650)=.0227, find σ.

Homework Equations

μ=expected value=mean

Variance=∫(X-μ)²fx(X)dx evaluated from -∞ to ∞

σ=√Variance

The Attempt at a Solution

I'm not sure what the relationships between the standard deviation and the probabilities given are.
My only guess is that P(X≤500)=.5 also fits the definition for the median of this function but I'm not sure where the median fits into the standard deviation either. Any help is appreciated!

 

[Ray Vickson]

Homework Statement

For a certain random variable X, P(X≤500)=.5 and P(X>650)=.0227, find σ.

Homework Equations

μ=expected value=mean

Variance=∫(X-μ)²fx(X)dx evaluated from -∞ to ∞

σ=√Variance

The Attempt at a Solution

I'm not sure what the relationships between the standard deviation and the probabilities given are.
My only guess is that P(X≤500)=.5 also fits the definition for the median of this function but I'm not sure where the median fits into the standard deviation either. Any help is appreciated!

The question as written does not allow for a unique solution. You need to assume a form of probability distribution, such as Normal or Poisson or Gamma or ... . I suggest you try it for the case of normally-distributed X.

 

[jaytech]

So you have a 50% chance of X being less than or equal to 500, and a 2.27% chance of it being greater than 650. That means there's a 47.73% chance for 500 < X <= 650. Now, knowing this you should be able to divide your integral into three separate integrals, as you now know the PDF values for each region.