Question

a)  The defect rate for a wire making process has a Poisson distribution with 1.23 defects per 1000 feet. Let X be the number of defects widgets in a randomly-selected 1000-foot length of wire. What is the probability that there will be no defects in that length of wire? State your answer rounded to three decimal digits.

b) Let X be the net weight of a randomly-selected cereal box. The distribution of net weight for this filling process is uniformly-distributed between 451.8 and 459.1 grams. What is the probability that a randomly-selected box will have a net weight less than 454 grams? State your answer rounded to three decimal digits

Answer 1

1).X : the number of defects widgets in a randomly-selected 1000-foot length of wire.

X~ poisson()

where, =  number of defects per 1000 feet = 1.23

the pmf of the distribution be:-

the probability that there will be no defects in that length of wire be:-

2).X : the net weight of a randomly-selected cereal box .

X ~ uniform (451.8,459.1)

the pdf of the distribution be:-

the probability that a randomly-selected box will have a net weight less than 454 grams be:-

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