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For the normal, Student’s t, Chi-square (χ
2
), and F distributions, which are
represented by functions UTPN, UTPT, UPTC, and UTPF in the calculator, the
inverse cuff can be found by solving one of the following equations:
• Normal, p = 1 – UTPN(µ,σ2,x)
• Student’s t, p = 1 – UTPT(ν,t)
• Chi-square, p = 1 – UTPC(ν,x)
• F distribution: p = 1 – UTPF(νN,νD,F)
Notice that the second parameter in the UTPN function is σ2, not σ
2
,
representing the variance of the distribution. Also, the symbol ν (the lower-
case Greek letter no) is not available in the calculator. You can use, for
example, γ (gamma) instead of ν. The letter γ is available thought the
character set (‚±).
For example, to obtain the value of x for a normal distribution, with µ = 10,
σ
2
= 2, with p = 0.25, store the equation ‘p=1-UTPN(µ,σ2,x)’ into
variable EQ (figure in the left-hand side below). Then, launch the numerical
solver, to get the input form in the right-hand side figure:
The next step is to enter the values of µ, σ
2
, and p, and solve for x:
This input form can be used to solve for any of the four variables involved in
the equation for the normal distribution.
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