Suppose that a company selects two people who work independently inspecting two-by-four timbers. Their job is to identify low-quality timbers. Suppose that the probability that an inspector does not identify a low-quality timber is 0.20. (a) What is the probability that both inspectors do not identify a low-quality timber? (b) How many inspectors should be hired to keep the probability of not identifying a low-quality timber below 1%? (c) Interpret the probability from part (a).

Accepted Solution

Answer:Step-by-step explanation:GivenProbability that an inspector doe not identify  low-quality timber=0.20(a)Probability that both inspector do not identify a low quality timber[tex]P=0.2\times 0.2=0.04[/tex](b)Let n be the no of inspector Probability should be less than  1%=0.01so [tex]\left ( 0.2\right )^n<0.01[/tex]Taking [tex]\ln [/tex]both sides[tex]x>\frac{\ln 0.01}{\ln 0.2}[/tex]x>2.861thus minimum value of x is 3(c)From part b it is clear that minimum 3 officer are required to to keep the low  quality timber below 1%on an average 2 officer are not sufficient to identify 4 low quality timber out of 100