Question

URGENT!! PLEASE ANSWER QUICKLY

John and Jane are working on a project, and all of their project meetings are scheduled to start at 9:00. John always arrives promptly at 9:00. Jane is highly disorganized and arrives at a time that is uniformly distributed between 8:22 and 10:31. The time (measured in minutes, a real number that can take fractional values) between 8:22 and the time Jane arrives is thus a continuous, uniformly distributed random variable.

What is the expected duration of time (measured in minutes, a real number that can take fractional values) John waits for Jane to arrive?

Round your answer to three decimal digits after the decimal point.

Answer 1

It is given that:

John and Jane are working on a project, and all of their project meetings are scheduled to start at 9:00. John always arrives promptly at 9:00.

Jane is highly disorganized and arrives at a time (measured in minutes, a real number that can take fractional values) that is uniformly distributed between 8:22 (502 minutes) and 10:31 (631 minutes).

Let the random variable X denotes the time at which Jane arrives for project meeting and has Uniform distribution.

The expected value of X can be obtained as:

Hence, the expected time at which Jane arrives is 9:27.

Since, John arrives promptly at 9:00, therefore, the expected duration of time (measured in minutes, a real number that can take fractional values) John waits for Jane to arrive is 27 minutes.