Question

6. Extra-credit problem: 6 pts] Let θ denote the unknown proportion of time that an airline operator is busy answering customers, where 0 <8 <1. To estimate 0, a supervisor observes the operator at times selected randomly and independently from other observed times. Let xi1 if the operator is busy at the ith observation and let x, 0 otherwise, i -1,.,n. If the supervisor uses #2X1+--+- to estimate θ, determine the value of n for which the error of eatimation is at most 0.05 with probability 0.95

Answer 1

Giiven thot θ denote the onknoon Proportion of time that on aïxline opevato busy ansuwering cu cuStomesS The evs< ot estmotion is at most o.o5 Tne probabilty s 0.a5 Since nptiox estimate oj P i9Knoion n- & Cea ence 32u.16 385