Re: HP 32sII Integration Error of Standard Normal Curve Message #3 Posted by Anthony (USA) on 13 Mar 2012, 10:28 p.m., in response to message #2 by Dieter
Oh, but that's how I entered the expression in my other calculators, too:
exp^(z^2/2)/sqrt(2*pi)
I get the correct 0.3413 result in all my calculators except the HP 32sII. I tried what you said, to input (z^2/s), that is, to factor out the 1 outside the (z^2/2) subexpression and the HP 32sII gives the correct 0.3413 result.
That leads to a troubling dilemma though...Why won't HP 32sII square the zvariable first then negate it, which is what it should do? Why is it negating z first then squaring it? In the expression (z^2/2), which is equivalent to 1*z^2/2, the order of operations clearly dictate that exponents/powers (i.e., z^2) have to be evaluated first before multiplication/division (i.e., *1 and /2)?
I'm looking at my HP 33s and HP 35s, and the expression I inputted is exp^(z^2/2)/sqrt(2*pi), and they're correctly honoring the order of operations by squaring z first then negating it; I don't have to clearly factor out the 1 outside of the expression: (z^2/2)
So, as a recap, by negating z first then squaring it, the expression exp^(z^2/2)/sqrt(2*pi) is essentially being evaluated as exp^(z^2/2)/sqrt(2*pi) by HP 32sII.
Thank you for telling me this, now I'll make sure to
That's how I entered the expression in my other calculators, too:
exp^(z^2/2)/sqrt(2*pi)
I get the correct 0.3413 result in all my calculators except the HP 32sII. I tried what you said, to input (z^2/2), that is, to factor out the 1 outside the (z^2/2) subexpression and the HP 32sII gives the correct 0.3413 result.
That leads to a troubling dilemma though...Why won't HP 32sII square the zvariable first then negate it (which is what it should do for the standard normal curve)? Why is it negating z first then squaring it (which is (z)^2 = z^2)? In the expression (z^2/2), which is equivalent to 1*z^2/2, the order of operations clearly dictate that exponents/powers (i.e., z^2) have to be evaluated first before multiplication/division (i.e., *1 and /2)?
The result 0.4767 is being obtained by integrating exp^(+z^2/2)/sqrt(2*pi) from z=0 to z=1.
I'm looking at my HP 33s and HP 35s, and the expression I inputted is exp^(z^2/2)/sqrt(2*pi), and they're correctly honoring the order of operations by squaring z first then negating it; I don't have to clearly factor out the 1 outside of the expression: (z^2/2)
So, as a recap, by negating z first then squaring it, the expression exp^(z^2/2)/sqrt(2*pi) is essentially being evaluated as exp^(z^2/2)/sqrt(2*pi) by HP 32sII.
Thank you for telling me this, now I'll make sure to add in extra sets of parentheses to make sure that HP 32sII is evaluating expressions correctly.
...
Hopefully I conveyed the problem clearly.
To sum up, the HP 32sII is evaluating the standard normal curve exp^(z^2/2)/sqrt(2*pi) as if it's exp^(z^2/2)/sqrt(2*pi), because HP 32sII is treating (z^2/2) as if it's (z)^2/2.
HP 32sII is not honoring the order of operations. In the expression (z^2/2) (which is the same as (1*z^2/2)), z has to be squared first then negated (multiplied to 1) because exponents/powers are evaluated before multiplication/division. HP 32sII is negating z first then squaring the result after, which is not what it should do, rather, z should be squared first then the result negated after.
