111k views
2 votes
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).

User Deitsch
by
7.3k points

1 Answer

2 votes

Answer:

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


P=0.2* 0.2=0.04

(b)Let n be the no of inspector

Probability should be less than 1%=0.01

so
\left ( 0.2\right )^n<0.01

Taking
\lnboth sides


x>(\ln 0.01)/(\ln 0.2)

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

User Alex Monthy
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories