(17B) Normal Distribution
04-01-2019, 12:15 AM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,046 Joined: Dec 2013
(17B) Normal Distribution
Normal Distribution

The following solver approximates the area of a normal distribution. The following equation uses L (Let) and G (Get), so this can be used for the classic HP 17BII and the silver HP 17BII+.

Code:
NORM: CDF=1-EXP(-X^2÷2)÷SQRT(2*PI)*(.4361836* L(T:INV(1+.33267*X))-.1201676*G(T)^2+.9372980*G(T)^3)

Instructions:

For x ≥ 0, enter x in ( X ) and then press (CDF) to solve.

For x < 0, enter abs(x) in ( X ), press (CDF) to solve, negate the result and add 1.

The area will be calculated from 0 (the center) to x.

Example 1: x = 2.5

2.5 (X), (CDF): Result: 0.99

Example 2: x = 1

1 (X), (CDF): Result: 0.84

Example 3: x = -1.5

(Algebric Mode)

1.5 (X), (CDF) [+/-] [ + ] 1 [ = ]: Result: 0.07

Source:

"Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphics, Transforms" Research & Education Association. 1984 ISBN 0-87891-521-4

Blog Entry: https://edspi31415.blogspot.com/2019/03/...andom.html
04-01-2019, 12:37 AM
Post: #2
 rprosperi Senior Member Posts: 3,818 Joined: Dec 2013
RE: (17B) Normal Distribution
(04-01-2019 12:15 AM)Eddie W. Shore Wrote:  The following equation uses L (Let) and G (Get), so this can be used for the classic HP 17BII and the silver HP 17BII+.

This equation may work properly on the Silver 17BII+ (I did not check it) but many equations that use L( ) and G( ) will not work properly on either the Gold or the Silver 17BII+ due to a bug in the solver when it was ported from the Pioneer series to the new h/w when the original 10BII and 17BII+ Gold were created. It was still not corrected when HP later introduced the 17BII+ Silver.

Let & Get in the Solver do work properly in the 18C, 17B, 27S, 19B, 19BII, and 17BII in all cases.

HP finally documented the Let and Get functions starting with the 10BII Silver and 17BII+ Gold manuals, and also the 17BII+ Silver, but it was not included in the original manuals for the older machines listed above (they sold the "Technical Applications" manual as a separate manual that documented Let/Get and other advanced solver features).

So in an ironic twist, Let and Get worked properly in the all machines which did not include documentation on how to use them, but they did not work properly in all the machines that did include them in the manuals.

--Bob Prosperi
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