Can you please help me with these 1. Sunita\'s job is to provide technical suppo
ID: 3205815 • Letter: C
Question
Can you please help me with these
1. Sunita's job is to provide technical support to computer users. Suppose the arrival of calls can be modeled by a Poisson distribution with a mean of 4.5 calls per hour. What's the probability that in the next 15 minutes there will be 2 or more calls?
2. The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson distribution to approximate the probability that among 7000 cars passing through this tunnel, at least one will have a flat tire.
Explanation / Answer
2 ans ) given that probability of car have flat tire through tunnel = 0.00004= 4*10^-5
probability among 7000 cars is given by = 7*10^3
mean = (4 * 10^-5) * 7*10^3 = 0.28
p(x >= 1) = 1 - p(x < 1) = 1 - p(x == 0)
by poission distrubition formulea we have
p(x) = ( (mean^x) / x! ) * exp(-mean)
p(x == 0) = 0.28^0 / 0! * exp(-0.28)
=0.7558
p(x >= 1) = 1 -0.7558 = 0.2442
1 ans ) given that poission distribution with 4.5 calls per hour
probability of next 15 min will be 2 or more calls
mu= 4.5 /hr
= 1- poission ( 4.5 / 6 , 1)
= 1-0.8598
=0.1402