Poisson Probability Problems

I am going to absolutely bomb my homework unless I get some help, it feels like every answer is wrong


1. A real estate office has been averaging 1.8 sales per day for the past several months. What is the probability that the office will make 4 sales today? .0723
2. A washing machine in a Laundromat breaks down an average of two times per month. What is the probability that the machine will break down more than 28 times in the next year? .1775
3. Flaws occur randomly in a particular fabric with a mean rate of occurance of 1.5 every 5 sqare yards. If you purchase 20 square yards of fabric, what is the probability that there will be at least 5 flaws in your fabric? .5543
4. A coil of wire has 500 metres of wire. Suppose there are 20 nicks (the most common problem with wire) are randomly distributed on a coil.
a) What is the probability that in a 50 metre length of wire there will be at least 7 nicks? .0011
b) What is the probability that in a 31 metre length of wire there will be exactly 3 nick(s)? .0920
5. Two students have started a business to seal driveways during the summer months. They rent a pickup truck and a power sprayer. With this they will use a tar based spray to seal asphalt driveways. Past experience has shown that the best time to sign up customers is to ring their doorbells between 5:00 and 8:00 p.m. on any weekday evening. Any jobs that they obtain will be completed the next day. In the months of June. July and August they find that they get an average of 2.9 customers per hour ringing doorbells.
a) What is the probability that they will get from 5 to 7 jobs in an evening of soliciting?
b) They charge $25 per driveway. If the truck costs $45 per day, and the spraying equipment costs $20 per day and the material to seal one driveway costs $6, what is the probability that they will make a profit on any given day.


These are my questions, couldn't even figure out how to answer the last 2. All of these were done using Ppd or Pcd but again I don't think I am inputting the correct values.


****ANY help would be greatly appreciated, even if it's just telling me that a question is wrong. Appreciate any help in advance

Many calculators will do Poisson distributions.

But, the formula is \(\displaystyle \frac{{\lambda}^{x}e^{-\lambda}}{x!}\)

So, for the first one \(\displaystyle \lambda =1.8, \;\ x=4\)

For the second one, you count up the probabilities from 0 to 28 and subtract from 1.

There are, on average, 24 break downs per year.

\(\displaystyle 1-\displaystyle \sum_{k=0}^{28}\frac{24^{k}e^{-24}}{k!}\)

The third one: since there are 1.5 flaws in 5 yds, you would expect 6 in 20 yards.

\(\displaystyle 1-\displaystyle\sum_{k=0}^{4}\frac{6^{x}e^{-6}}{x!}\).

4a is done the same way. If there are 20 nicks in 500 meters, how many do you expect in 50 meters?. This will be your lambda. Sum them up from 0 to 6 and subtract from 1.

Sorry, I did not get into the last two. They require a little more thought and I am tired.