Question

A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work No. of red lights Probability o 1 2 3 4 5 OS 25 30 30.5 TOS Note that the standard deviation of the above probability distribution is SDX) 1.27 Question 1. What is the spected number of red lights at which she will stop on her way to work? use I decimal place in your answer) Question 2. Suppose each red light delays the commuter 1.5 minutes. What is the standard deviation of the number of minutes that she is delayed by red x us 3 decimal places in your answer) e ?

Answer 1

(1) Let us assume that X be the number of red lights. The expected number of red lights at which the commuter will stop on her way to work is given as follows: E(X)=Xx p(x) =0(0.25)+1(0.25)+2(0.30)+3(0.20)+4(0.15)+5(0.05) = 2.3 Thus, the expected value is (2) Let Y be the delay due to each red light, then Y=1.8 X. V(Y)=V (1.8X) =1.82 V(X) = 3.24(SD (-X))? =3.24(1.27) =5.2258 SD(Y)=15.2258 = 2.286 The standard deviation is