This article features how to use the functions UTPN, UTPC, UTPF, and UTPT in a solver.

Working with the Normal Distribution. 

The UTPN, when given mean, variance, and the x-point, gives your the upper tail probability on the normal distribution curve.

For example, if I have a mean=0, variance=1, and an x-point=1,

UPTN(0,0,1) returns (approximately) .1587

(RPN Mode:  mean, variance, x-point, UPTN)

Under the normal distribution curve, the area between 1 and infinity is .1587.  Or, 15.87% of all data lies more than 1 variation from the mean.

But what if I know the area (or proability) and I'm trying to find the x-point?

Unfortunately, if I try to type 'P=UTPN(m,v,x)', I get an error.  (Invalid Syntax)

We still can find a way to find the x-point.  We in this case use a program.

The program is:  << <<  M  V  X  UTPN P - >> STEQ 30 MENU >>  I have it stored as NORMSLV.  (NORMal distribution SoLVer)

The program stores UTPN(M,V,X)-P=0 in the variable EQ and calls up the Solver (30 MENU).

To enter the data, just press the soft key (F1-F6).

To solve for a variable, press LEFT SHIFT, soft key (F1-F6).

Example:  I have data that is distributed like the normal distribution.  From the data I have Mean = 30.62, Variance = 11.24.  What would be the minimum point (score) to be in the upper 15% tile.

1.  Run the program NORMSLV.

2.  Store 30.62 into M, 11.24 into V, and .15 into P.

3.  Press Left Shift, X.  The HP 50g returns X:33.7347579024.    (so approximately 33.7348 to get into the upper 15%).

Do not forget to clean up by purging M, V, P, and X.

Variables used with other Upper Tail Probability Functions: (sub for the equation part)

UTPT (Student's T Distribution):  <<  D  T  UTPT P  -  >>    (D = degrees of freedom, T =  t-point)  (mean is assumed to be 0 and variance is assumed to be 1)

UTPC (Chi-Sqaure Distribution):  << D T  UTPC P - >> (D = degrees of freedom, X = x-point)

UTPF (F Distribution):  << D1  D2  F UTPF P - >> (D1, D2 = degrees of freedom, F = f-point)

E. Shore