I need to find probability given only the mean.

ex- mean number of occurences in an hour is 2. What is the probability that it will happen 5 times in a given hour? Do I use 60 minutes as the number of times it is possible, 5 as the required number and .5 for the probability that it will or will not happen on a given minute? I cant get this one. Thanks.

 

Megastat said 10.162% using binomial distribution

 

It has been a decade since I took statistics, but here are my ideas anyway on how to visualize and set up the problem.

Imagine a bell curve situated in the upper right quadrant of the X-Y axes. The X-axis represents the number of occurances per hour, and the Y-axis represents the probability of occurance.

The curve peaks at X=2 because 2 is the mean number of occurances, so all the values of X will cluster around that number. Within one standard deviation of the number 2, 66% of all occurance rates will fall - this means that 66% of the area of the bell curve will be within one standard deviation of the mean.

Within two standard deviations, 95% of all occurance rates will fall, and within three standard deviations of the number 2, 99.5% of all occurance rates will fall.

(Draw this out and it will make more sense.)

Your job would be to find the Y-value of the curve when X=5. I'd imagine that would involve a conversion to a Z-score if I remember correctly.

But I'm sure the problem has nothing to do with breaking it down to 60 minutes or assigning a 50% probability of yes/no to each minute. Rufushusky's answer above checks out with my common sense; X=5 will be down the curve quite a bit.

 

You guys are makin my head hurt.

 

About 10 is what I came up with. I think the prob of it happening is 1, not 0.5. It seems like either it would happen or it wouldn't. It also depends as how they defined the event.

 

There isnt alot of clarity in the question as to definition of measuring units. I am assuming I should be using 60 minutes. This is my last class and as luck would have it, the arent offering it at the school so I have to take it online. I feel like I am trying to teach myself to eat razor blades. Anyhow, thanks for the info and I will keep plugging at it.

 

On second thought, I think you don't have enough information to solve the problem. You could solve it if you had the mean and standard deviation, but since you don't have the standard deviation, you don't know the shape of your bell curve and thus can't figure out the probability of X=5

Use this applet to see what I'm talking about:

http://davidmlane.com/hyperstat/z_table.html

Basically, if the SD is small, the numbers will be clustered around 2 very tightly and 5 will be an extreme outlier, so the probability that X=5 will be very small. if SD is huge, then there's a great chance 5 will be within 1 SD of the mean, so the probability that X=5 will be large.

 

I figured it out using Excel Poisson calculator. All I needed was to use the Mean of 2, x=5 and the and set the Poisson probability mass function to false. Answer was .0361. Thanks.

 

yall know that 80% of all statistics are just made up on the spot dont ya????