In: Statistics and Probability
You have reasons to believe that your plane will arrive at a time that is uniformly distributed between 10:30 and 10:50. By 10:37, you’re still waiting for the plane.
a. What is the probability that you will have to wait at least another 5 minutes for the plane? Hint: Draw the graph (with the x and y axis labeled) and find the area being described.
b. Find the mean and standard deviation of the situation described above.
Answer:-
Given that:-
Let random variable X denote the arriving time of plane .
So, X is uniformly distribution between 10:30 and 10:50.
So, pdf of X is given by
(a) Probability that you will have at least five minutes
b)Mean
Standard deviation
[If
then,
Hence Mean=10:40 S.D]
i.e., Mean time =10:40
Standard deviation =5.7735