Question

question 19 b

n=114

p=0.14

question 21

design life (50) months

-2 motors?

-3 motors?

independentiy uf dle 19. What is the probability of having not more than 20 but not less than 10 failures if n Section 2.10) a Using the binomial distribution b Using the normal approximation 20. The life of an electronic controller is distributed lognormally, with the parameters μ = 20 and What is the probability that a controller will last (a) at least 50 h? (b) at least 200h? 21. A commercial washing machine has a non-repairable motor with a constant failure rate of 0.08 per year. The service organization has purchased two spare motors. If the design life of the machine is 7 years, what is the probability that two spares will be adequate. Hint: assume Pois distnbution but not less than 10 failures if n-100, p.1 Question ) 2 motoa

Answer 1

Problem 19 b2 n 114 ps 0-14 Mean (ll) = 114x014 = 15.96 Std Deviation ) np 15.96 3.994 Required Probablity Calculation of Normal variates '= 20-1596 3.994 At χ= 20, Z1 = 1-011 -149 0 O -z 8.994 From Normal Distribution table Type Z P[OSzs1490-4319(Area corres ponding to 2 1 49) P Tos2SO]0 3438 (Area corresponding to 2-I-o1 Due to symmetrical nature of normal Distribution curve Area T0 4319 0.3438 Area Required probablity te P4914319 +0 3438 0-7757 = ㄱ7.57%

Problem 21 Given: Failures in iyr 008 Foilures in 50 months 0 08x500 34 12 (AT) Probablity that 2 motors will be sufFicient 2 motors will be sufficient When no. of failures (n) 드2 e n o ori or2. during life time of 4167yrs or 5omonths n! Pr 리):(034), e-o34 P(n-1)(034)' e 0 2420 0 0411 2 1 Rn-2) P6-o)+ Rn,+ Required Proba blity- 0.7117 t 0.2420 + 0.0411 = 0.9948 99.48 Probablity that 3 motors woill be sufficient 03 43x e-084 h-3) = 3! Rn-3) P(n=0)+ P(n=D+ P6-2) t Required Probablity = = 0-7117 t 0.2420 + 0.04, l t 0.0046 0.9994 = 99.94