Question

The number of flaws in the castings used in internal combustion engines is known to follow poisson distribution with a mean 0.01 flaws per cubic foot of the casting if a casting with a volume of 50 cubic foot of the casting. if a casting with a volume of 50 cubic feet is used in an I.C engine, determine the following:

a. probability that there are no flaw in the 50 cubic feet casting

b. if 5 of the 50 cubic feet casting are bought by a power generating company the probability that none of the castings has a flaw

c. if 5 of the 50 cubic feet casting are bought by a power generating company the probability that at most one of the castings has a flaw

Answer 1

a)

mean = 0.01 flaw/cubic foot

for 50 cubic foot

$\lambda$ = 0.01 * 50 = 0.5

P(X = 0) = e^(- $\lambda$) = e^ ( - 0.5) = 0.606530

b)

Y = number of casting which has flaw

Y follow binomial distribution with n = 5, p = 1 - 0.606530

P(Y = 0) = q^n = (0.606530 )^ 5

= 0.082084

c)

P(X <= 1)

= P(X = 0) + P(X =1)

= 0.082084 + 5 * ( 1 - 0.606530 ) * 0.606530 ^4

= 0.348334

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