Question

question of stats probability:
Failures of the steering mechanism of a car occur at random with, on the average, 1 failure in 300,000 miles. Use the Poisson distribution to find, to four decimal places, the probability that (a) the car completes 45,000 miles without a steering failure, (b) there are 3 or more failures in 45,000 miles. Two cars, X and Y, with this type of steering mechanism, are bought, and, while X is running its first 45,000 miles, Y will run 150,000 miles. Find the probability that during this period there will be not more than one steering failure altogether

Answer 1

a) for 45000 miles ; expeced failure =45000/300000=0.15 =

therefore probability that the car completes 45,000 miles without a steering failure =P(X=0) =

=e^-0.15 =0.8607

b)

probability that 3 or more failures =P(X>=3) =1-P(X<=2) =1- =1-0.9995=0.0005

c)

for X expected number of failure =0.15 =1

for Y expected number of failure = 150000/300000 =0.5 =2

for combined failure parameter =1+2 =0.15+0.5 =0.65

therefore  probability that during this period there will be not more than one steering failure altogether

=P(X+Y<=1) = =0.8614