Normal Distribution
The resistance R of electrical resistors produced by a particular machine may be described by a normal distribution with mean Rm and standard deviation σ.
The production cost for one resistor is C, and the price is 5C if R = R0 ± ?1, and 2C if R0 - ?2 0 - ?1 or R0 + ?1 0 + ?2. Resistors outside these limits cannot be sold.
(a) Determine the profit P per resistor produced for Rm = R0, ?1 = a1 R0, ?2 = a2 R0, σ = b R0. Use the distribution function ψ0.
(b) Use Table 1.2 to compute the numerical values of P for a1 = 0.01, a2 = 0.05, b = 0.05.
(c) Show that the probability density (5.7.1) has points of inflection (Le., second derivative equal to zero) at x = a ± b.
