Ok I know that the probability of a Z-score of 4 is .49997. I simply want to find out HOW this number was calculated from a Z-score chart that only goes up to like 3.49.
Z-score charts typically only go up to 3.4 and 3.49, so how do I find the probability of a Z-score equaling 4?
*NOTE* this is finite math. please be descriptive as possible and refrain from statistics and calculus solutions.
Ok, now you have provided more information, this is helpful.
The value 16.5 is to the right of 16, but to answer the entire question we need to know even more. Lets say its looking at the probability that the mean is less than 16.5 then
In the case that
How did I get this value for ? Well consider the 68-95-99.7 percent rule for the normal distribution. It states that you should now be able to convince yourself that
How about finding the probability that the sample mean is between 15.7 and 16.5.
random sample of 64
15.7 has Z=-2.4
16.5 has Z=4
Standard error of the mean=.125
Looking at the Z-chart, I find the area between the raw scores of 15.7 and 16 to be .4918
Now I must find the area between 16 and 16.5 so I can add that value to .4918 and get the sum of the two areas.
How should this area be found if the raw score of 16.5 gives a z-score of 4. Am I to use the 68-95-99.7 percent rule?
your probably right. Im just new to it all.
I found the the area between -2.4 and 0 to be .4918. This was done first by converting the raw score of 15.7 to a z-score of -2.4 by using the formula Z= X-M/standard error of the mean
Now, to be consistant, I used the same formula to convert our other raw score of 16.5 to a z-score of 4.
Ok now finding the area between -2.4 and 0 was simply a matter of looking at the z-score chart, finging the 2.4 and observing the coresponding area of .4918
Now, Its understood that we need to find the area between 0 and 4. The problem was that the z-chart ONLY goes up to Z-score 3.49, not 4.
The area between 0 and 4 is .49997. I only know this much because the answer in the back of the book is .99177, which means that
.4918 + .49997 = .99177
Its not a matter of me finding the answer though. I need to find out a more direct way of looking at the z-chart and finding the area when the z-score is 4. From the computation .4918 + .49997 =.99177 , its already clear that my math is correct since .99177 is the answer listed in the back of the book. And the fact the the z-score of -2.4 yeilds .4918, as clearly seen on the z chart.
The mystery to me wrapped around computing the area between 0 and 4, since the z-chart ONLY goes up to 3.49
I can see this is frustrating, just don't read too much into it.
The normal distribution is a total contridiction. Consdering You have a contiuous function all > 1 on with a 'finite' area of 1 underneath, you can never understand it fully.
So my advice is to be at peace with it. There are bigger fish to fry in the big world that is probability
22.214.171.124.1. Cumulative Distribution Function of the Standard Normal Distribution
The link above is what I was looking for; The area between the mean and a Z-score of 4 is listed as .49997 thank you for your patience though. I am still pretty new at this ...obviously.