A small company has 12 servers set up independent of each other. The servers are
ID: 3230104 • Letter: A
Question
A small company has 12 servers set up independent of each other. The servers are getting old an each as a probability of breaking equal to 0.15. Use this to answer the following questions: a. What is the mean number of broken servers on any day. b. It only takes one server to keep the company's website up. Find the probability that the website is up and running. c. The company calls tech support if at least 10 servers are down. What is the probability they need to make that call? d. What is the standard deviation for the number of broken servers? Norma is considering going to the fair. She estimates her chances of going are one half. If she does go the chances that she will have a good time are two thirds. What is the probability she will go to the fair and have a good time?Explanation / Answer
Probability of breaking,p=0.15
n=12
a) Mean servers broken=np=12*0.15=1.8
b) Required probability =(1- P(all servers are broken) = 1- (0.15)^12 = 0.99999999987
c) Reuired probability =P(10 are down)+P(11 are down)+P(12 are down) = 12C10 * (0.15)^10*(0.85)^2 + 12C11 * (0.15)^11*(0.85)^1 + 0.15^12 = 66 * (0.15)^10*(0.85)^2 + 12* (0.15)^11*(0.85)^1 + 0.15^12 = 0.000000283
d) Standard deviation = sqrt(npq) = sqrt(12*0.15*0.85) = 1.2369