Question

(A) Information delivered to the senior management of a large manufacturing concern revealed that the number of stoppages of the production line follows the Poisson law with an average of 1.5 stoppages per 500 hours of operation. (a) Compute the probability that more than one but fewer than five stoppages occur in 500 hours of operation. (b) Compute the probability that at most three stoppages occur in 1,000 hours of operation. (c) Compute the probability that the production line experiences one stoppage in 500 hours of operation followed by two stoppages in the subsequent 500 hundred hours of operation. Explain your reason for using the method you adopted in your computations. 3.(13) The probability that an employee of the manufacturing concern under consideration is fired because of gross negligence is 0.2%. Use an appropriate approximation to compute the probability that in a random sample of 1,000 employees more than two will be fired because of gross negligence.

Answer 1

a)

X follow poisson distribution with mean 1.5

P(1 < X < 5)

= P(X <= 4) - P(X <= 1)

= =POISSON(4,1.5,1)-POISSON(1,1.5,1)

=0.4236

b)

Y follow poisson distribution with mean = 1.5/500 * 1000 = 3

P(Y <= 3)

=poisson(3,3,1)

= 0.6472

c)

P(X = 1 in first 500 hours and X = 2 in next 500 hours)

= P(X = 1) * P(X = 2)

x	P(X = x)
1	0.334695
2	0.251021

hence required probability =   0.3347 * 0.2510

= 0.084