Answer:
a
Step-by-step explanation:
We should first calculate the average number of checks he wrote
per day. To do that, divide 169 by 365 (the number of days in a year) and you get (rounded) 0.463. This will be λ in our Poisson distribution. Our formula is

. We want to evaluate this formula for X≥1, so first we must evaluate our case at k=0.

To find P(X≥1), we find 1-P(X<1). Since the author cannot write a negative number of checks, this means we are finding 1-P(X=0). Therefore we have 1-0.3706=0.6294.
There is a 63% chance that the author will write a check on any given day in the year.<em />
Answer: 0.01708
Step-by-step explanation:
Given : If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year.
i.e. the probability that house damaged buy fire in a year : 
The formula for binomial distribution is given by :-

Now, the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year (put n=14 and x=2), we get

Hence, the required probability = 0.01708