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).

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nuuk nuuk · Answer 1 · 2019-10-16T11:23:17+02:00

Answer:

Step-by-step explanation:

Given

Probability 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%=0.01

so [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>2.861

thus 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