Question

1)The annual number of industrial accidents occurring in a particular manufacturing plant is known to follow a Poisson distribution with mean 12.

What is the probability of observing of observing exactly 12 accidents during the coming year?

What is the probability of observing no more than 12 accidents during the coming year?

What is the probability of observing at least 15 accidents during the coming year?

What is the probability of observing between 10 and 15 accidents (including 10 and 15) during the coming year?

Find the smallest integer k such that we can be at least 99% sure that the annual number of accidents occurring will be less than k.

Answer #1

Let X denotes the annual number of industrial accidents occurring in a particular manufacturing plant.

X ~ Poisson(12)

The pmf of X is

The probability of observing of observing exactly 12 accidents during the coming year

The probability of observing of observing no more 12 accidents during the coming year

The probability of observing at least 15 accidents during the coming year

The probability of observing between 10 and 15 accidents (including 10 and 15) during the coming year

To find k such that

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