How to get equivalent of binomial probability on a continuous scale?

S

scrivener

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A probability question:

If each trial with a binomial result has a probability of success of 50%, the probability of succeeding 3 or more times in 5 trials is 50% ... 6 or more times in 10 trials is .377 ... 30 or more times in 50 trials is .101, etc. So my binomial calculator tells me.

How does one compute analogous probability for success on a scale?

E.g., suppose in a random trial one picks a number in the top 33% of a population (about a half standard deviation or more above average). The probability of that is 33%.

But how does one figure the probability of in, say, five independent trials picking numbers that on average have a value in the top 33%? (Not all being in the top 33%, that would be 0.33^5, but which average being in the top 33%.) Or of in 10, 15, trials picking numbers that have an average value in the top 33%?

I've looked around for the answer and as this seems a rather basic question have been surprised not to find it. Or maybe I'm just too innumerate to recognize it when I see it.

Thanks in advance to anyone who straightens me out on this.

Also thanks to anyone who can point me to a good web site that discusses this particular issue and related ones on a basic level.
 
Nothing to straighten. The answer is right before you.

Selecting a value at random, and considering whether it is in the top 1/3 is a binomial experiment. The underlying distribution is of little concern.
 
tkhunny said:
Nothing to straighten. The answer is right before you.

Selecting a value at random, and considering whether it is in the top 1/3 is a binomial experiment. The underlying distribution is of little concern.
Click to expand...

Thanks for the reply, but either I'm missing your point or I expressed my question poorly.

I'll try to make it more explicit:

Say there is a population of items with an average value 50, standard deviation of 20.

1) Randomly sample an item, find its value is 60. That's half a standard deviation above average, so the probability of pulling that value or higher is 31%.

2) Randomly sample five items, find their values are 40, 55, 60, 70, and 75 (average 60). The probability of pulling these five values (or higher) is ...??? I dunno.

I am trying to learn the way to calculate #2.

Thanks in advance.
 
Why do you care what the average is? Do you want p(X > min(whatever I drew))?
 
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