HP F2216A hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 271

To start: R M B Y ( yˆ when X=37) X ( xˆ when Y=101) Logarithmic X L 0.9965 -139.0088 65.8446 98.7508 38.2857 Exponential X E 0.9945 51.1312 0.0177 98.5870 38.3628 Power X P 0.9959 8.9730 0.6640 98.6845 38.3151 Normal and Inverse-Normal Distributions Normal distribution is frequently used to model the behavior of random variation about a mean. This model assumes that the sample distribution is symmetric about the mean, M, with a standard deviation, S, and approximates the shape of the bell-shaped curve shown below. Given a value x, this program calculates the probability that a random selection from the sample data will have a higher value. This is known as the upper tail area, Q(x). This program also provides the inverse: given a value Q(x), the program calculates the corresponding value x. y "Upper tail" area Q [x] x x ³ Q(x) = 0.5 − 1 e dx x −((x −x )÷σ )2 ÷2 σ 2π x This program uses the built-in integration feature of the HP 33s to integrate the equation of the normal frequency curve. The inverse is obtained using Newton's method to iteratively search for a value of x which yields the given probability Q(x). Statistics Programs 16-11