Question

A maintenance worker in a large manufacturing plant knows that a filling machine breaks down on average 3 times per month. Assume these break downs occur randomly and independently of one another.

a. If the random variable X is the number of times the machine breaks down, identify the distribution of X and state the value/s of its parameter/s

b. Calculate (using the appropriate statistical tables) the probability there are less than three breakdowns in the next month.

c. Calculate (using the appropriate statistical tables) the probability of seven breakdowns in the next two months.

d. Verify your answers to parts b. and c. using the appropriate Excel statistical function and demonstrate you have done this by including the Excel formula used.

Answer 1

a) X is the number of times the machine breaks down,

x follows Poisson distribution with parameter λ = 3

P( x ) = , x = 0,1,2,3...

b) P( x < 3 ) = P( x ≤ 2 )

P( x = 0 ) = 0! = 1

P( x = 0 ) = 0.0498

P( x =1 ) = = 0.1494

P( x = 2 ) = = 0.2240

P( x < 3 ) = P(0) + P( 1) + P( 2)

P( x < 3 ) = 0.4232

c) 3 breakdowns in one months , so there are 3*2= 6 breakdown in two months , so λ = 6

P( x = 7 ) =

P( x = 7 ) = 0.1377

d) Using excel function =POISSON.DIST(x,λ,cumulative)

P( x < 3 )   =POISSON.DIST(2,3,TRUE) = 0.4232

P( x = 7 ) =POISSON.DIST(7,6,FALSE) = 0.1377