Probability - Need a help to solve the below question

raghu_1968

Involved In Discussions
#1
Need a help to solve the below question, which came during the training and it is part of the assessment.

"A small construction crew in northwestern Canada is about to start road work on a mining road. The work is not too difficult and it will only take one day. Since tis road is in a pretty remote area, not many vehicles drive on it. The amount of daily traffic follows a uniform distribution with daily vehicles ranging from 5 to 14.
Given this discrete uniform distribution, what is the probability that the number of cars stopped by this construction will be 5 to 6?

What is the probability that the construction crew will stop less than 6 cars?"

Thanks.
 
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Bill Levinson

Industrial Statistician and Trainer
#2
For a distribution from 5 to 14 inclusive, there are 10 possibilities. The chance of getting 5 or 6 is therefore 20%. The chance of less than 6, i.e. 5, is 10%. The statement "less than" indicates that the interval does not include the upper number.
 

Bill Levinson

Industrial Statistician and Trainer
#4
The uniform distribution says there is an equal chance of getting 5, 6, 7, ... 14 vehicles which means each outcome has a 1 in 10 probability. The chance of 5 or 6 is therefore 2 out of 10.

This is actually a very simple problem because it does not use the usual Poisson distribution for random arrivals (for which we would need the average number of vehicles per day), although the Poisson can be calculated easily in Excel as well as Minitab or StatGraphics.
 
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