# Probability problem about a parking lot

We want to design a parking lot for a group of 200 apartments still under construction. It is known that for each department (from city statistics) the number of cars will be 0, 1 and 2 with probabilities 0.1, 0.6 and 0.3 respectively. It is desired that with 95% certainty there will be space available for all cars when apartments are sold. How many parking spaces should be built?

• Welcome to MSE. You'll get a lot more help, and fewer votes to close, if you show that you have made a real effort to solve the problem yourself. What are your thoughts? What have you tried? How far did you get? Where are you stuck? This question is likely to be closed if you don't add more context. Please respond by editing the question body. Many people browsing questions will vote to close without reading the comments. – saulspatz May 18 at 15:08
• What have you tried? What is the expected number of cars? What is the variance on the number of cars in one apartment? – Ross Millikan May 18 at 15:32
• These are the only things that give me on the problem, i have nothing else – Luis Fernando Palafox Orozco May 18 at 18:15
• I would say, Ross Millikan asks if you have already calculated this data. – georg May 19 at 0:56
• @RossMillikan Oh, I didn't get that, sorry. Well, making the operations, i got that the expected number of cars is 1.2 and te variance on the number is 0.36 The thing now is that how do I express de 95% to get the result? – Luis Fernando Palafox Orozco May 19 at 2:59