Question

"SUPERCALIFRAGILISTICOEXPIALIDOSO" is a manufacturing company of resistors which are known to have an exponential failure rate distribution failure rate= 9.09 x10 -5 exponent

A-what is the probability any resistor will still be working after 6000 hours of use

B- given that a resistor has been working for 4,500 hours, what would be the probability that it would survive 2000 hours more of use

C- what is the probability it will fail within 5,500 hours of use

Answer 1

Answer:

Given,

Failure rate = 9.09*10^-5

a)

To give the probability any resistor will still be working after 6000 hours of use

Required probability = e^-t

= e^-(9.09*10^-5*6000)

= 0.5796

b)

Probability working for 4500 hrs = e^(-9.09*10^-5)*4500

= 0.6643

Probability that it will work for 6500 hrs

= e^(-9.09*10^-5*6500)

= 0.5539

Required probability = [(1-0.5539)-(1-0.6643)]/0.6643

= 0.1104

c)

To give probability it will fail within 5,500 hours of use

= 1 - e^-t

= 1 - e^-(9.09*10^-5*5500)

= 0.3934