Average probability question

[mrmat45]

Hi so I'm stuck on this weird question for my exercise.

Q is Daves Boat company sells on average 3 boats a day. How many boats would he have to sell on average per day so that the probability of selling no boat on any given day is less than 5%?

Any help would be appreciated thank you.

 

[Steven G]

You asked for help but failed to say what type of help you need. Where are you stuck? Can we see what you have tried? It is hard to help you if we have no idea where you are in the problem.

 

[mrmat45]

You asked for help but failed to say what type of help you need. Where are you stuck? Can we see what you have tried? It is hard to help you if we have no idea where you are in the problem.

Okay sorry, I've tried multiple amounts of things, what I'm stuck on Is how to approach the question. Many of the formulas on the probability that I've got always have a basis of n. I'm confused about the wording of the question when it talks on less than 5% does it mean p(x>5)? I've tried multiplying the average by 7 stating it as a week then timing it by 0.95, but I'm still unsure on whether or not this is the correct approach.

 

[mrmat45]

I have actually solved the question now, it turns out it was a Poisson distribution, in which the mean being 3, and x being in the statistics table of the probability above 0.95% which turned out to be 6 with a probability of 0.96%.

Thanks anyway!

 

[Steven G]

Where are you getting 0.95% from? You do realize that 0.95<1, so 0.95%<1%

Why would 5% turn into p(x>5)?

 

[mrmat45]

Where are you getting 0.95% from? You do realize that 0.95<1, so 0.95%<1%

Why would 5% turn into p(x>5)?

I was mixing up formulas, it was completely wrong. p(x>5) doesn't make any sense. With the mean provided Poisson(3) and limited information, but being allowed to use statistics charts I was able to identify that x=6 is just over 95% in terms of probability. So I came to the conclusion that 6 boats sold is greater than 0.95%. Thus Daves boat company would have to sell 6 boats on any given day to ensure the probability of selling no boat being less than 5%.