In order to etch an aluminum tray successfully, the pH of the acid solution used must be between 1 and 4. This acid solution is made by mixing a fixed quantity of etching compound in powder form with a given volume of water. The actual pH of the solution obtained by this method is affected by the potency of the etching compound, by slight variations in the volume of water used, and perhaps by the pH of the water. Thus, the pH of the solution varies. Assume that the random variable that describes the random phenomenon is gamma distributed with a = 2 and β = 1.
(a) What is the probability that an acid solution made by the foregoing procedure will satisfactorily etch a tray?
(b) What would the answer to part (a) be if a = 1 and β = 2?