normal distibution standard deviation

[mittman84]

I feel really dumb asking this question, but it is in my assignment that is due tomorrow and i am drawing a blank, and i have to figure out all this stuff by myself since my teacher is worthless. In in a certain normal distibution of X, the probability is .5 that X is less than 500, and the probability is .0227 that X is greater than 650, what is the standard deviation of X?

[Indiana]

Recheck ur post. U left off the number after the decimal..

Indy

[mittman84]

thank you, should be good now

[edtost]

well, you have:


for two observations of x, and know all parameters except for mu and sigma, which are the same for both observations. plug in numbers, solve for mu, set the expressions for mu equal to each other, solve for sigma.

edit: that's the pdf, so you actually have the integral of that for two observations.

edit edit: one of your observations is the mean. this makes the problem much easier.

[mittman84]

i came up with 75...does that seem right?

[edtost]

yup.

based on what the answer turned out to be, can you think of an easier way to do the original problem than doing out all the calculations?

[mittman84]

yes, z=(X-mean)/sd used the z table to find z=2.0 at .9773
so 650-500/sd = 2 solve and sd =75 that means 650 is two standard deviations from the mean, and because it is normal that will be 95% of the values. It is not exactly 75 because if rounding errors when using the z-table but 1-2*.0227=.95(roughly)tells that 650 is roughly 2 standard deviations from the mean, and mean =500