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Standard Normal Distribution
08202016 02:56 AM
Hi,
I am trying to solve the following equation:
X  N(50,15^2) Find Pr(50<X<70)
When I type the above into the calculator the following occurs:
I don't understand why I get an 'erf' rather than a decimal answer.
Can someone please help me with using the standard normal distribution function on HP Prime calculator.
Thanks,
Arthur
Solved! Go to Solution.
08202016 12:17 PM  edited 08202016 05:21 PM
Hi!, @Athanasios:
1) Approximate Mode.
2) Exact Mode.
erf : Returns the floating point value of the error function at x=a.
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
08202016 06:18 PM
Hi Make,
Thank you very much.
Can you please direct me to an explanation of 'erf' and the concept behind exact values (on the HP Prime)?
Is there anything I can read to help me understand this mathematical concept and why certain mathematical applications require different accuracy calculator settings, so I know how to set my calculator accordingly.
Regards,
Arthur
08202016 06:29 PM
Hi!, @Athanasios:
See, the description, of 'erf' by Tim Wessman, from ... http://h30434.www3.hp.com/t5/Calculators/HPPrimeerffunction/tdp/5047983
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
08222016 01:20 PM  edited 08222016 01:29 PM
Please do not change your CAS settings as described. It generally makes more problems then helps until you understand how things are working a bit more. Default settings are nearly always going to be better for most users.
Basically, the reason this is happening is because you are in the CAS screen. Click home, try it again, and you'll see it does come out a decimal. Putting a decimal value at the end of one of your integers in the CAS screen would ALSO return a decimal result (as you are telling the CAS "please calculate this using apprixmated numerical values since I gave you an approximate numerical value with a decimal"), as would hitting the SHIFTENTER function to approximate the last calculation after you get that result. Any of those are better solutions instead of changing settings like described.
As to what the erf( ) is, that is actually the way in which normal distributions are calculated! See this link for a great description: http://mathworld.wolfram.com/NormalDistributionFunction.html
Quoting from that page: "Neither nor erf can be expressed in terms of finite additions, subtractions, multiplications, and root extractions, and so must be either computed numerically or otherwise approximated."
In essence, the CAS is giving you the exact, symbolic representation of your normal distribution using a function that represents a certain operation. These types of "special functions" become more common in higher math/engineering type calculations.
When talking about exact/approximate, mathematicians are referring to the idea that something is a "perfect representation of the concept of that thing" or just a "number that is close enough to it". For example, +infinity is a concept that the CAS actually can understand, but a normal calculator couldn't  it couldn't hold a number large enough to be "infinite". Yet in many cases, just putting in a really big number in the calculation is "good enough" to represent the idea of positive inifinity.
Another good example of this is pi. Pi itselft cannot be represented as a perfect decimal number, but in most cases a rounded off value is "close enough". The Prime in CAS mode takes any perfect integer with no decimal to be the "idea of that number". For example SQRT(2) will return SQRT(2) in the CAS screen. There isn't a number that can simplify further down into. If you try doing SQRT(2.) (< note the . after the two), you are really saying "take the square root of the number that is 'close enough' to the perfect value of 2". The calculator then returns a number that is the square root "close enough" to the actual perfect, exact result.
If you do get an exact result and want to see the decimal approximation, just press SHIFT ENTER. That little squiggly equal sign is the mathematical symbol for "approximates to".
As to the last question, use this rule of thumb to help you as you get going  if you are trying to get an approximate decimal number result, the home screen is where you should be working. If you are wanting exact, symbolic algebra results, the CAS screen is where you should work. If you are in the CAS screen and want a decimal result, press shift ENTER to run the "approx" command which will do a one time evaluation of your last result to a decimal. Make sense?
Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
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