Question

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 1

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