ABC Inc. supplies circulators for commercial furnaces. If the circulator fails b
ID: 3312237 • Letter: A
Question
ABC Inc. supplies circulators for commercial furnaces. If the circulator fails before the furnace reaches 4,000 hours of operation, the company must replace it at no cost to the furnace owner. The circulator will last an average () of 5,500 hours with a standard deviation of 1,000 hours and has a normal distribution.
Determine: ( a) What is the probability that a circulator will be replaced at no cost to the furnace owner? ( b) What is the probability that a circulator will fail between 3,500 and 4,000 hours?
Explanation / Answer
Mean is 5500 and s is 1000
z is given as (x-mean)/s
a) P(x<4000)=P(z<(4000-5500)/1000)=P(z<-1.5) =1-P(z<1.5), from normal distribution table we get 1-0.9332=0.0668
b) P(3500<x<4000)=P((3500-5500)/1000<z<(4000-5500)/1000)=P(-2<z<-1.5) or P(1.5<z<2) or P(z<2)-P(z<1.5)
from normal distribution table we get 0.9772-0.9332=0.044