Question

In: Statistics and Probability

You have reasons to believe that your plane will arrive at a time that is uniformly...

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.

Expert Solution

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

orchestra answered 1 year ago

Romeo and Juliet have a date at a given time, and each will arrive at the...

Romeo and Juliet have a date at a given time, and each will arrive at the meeting place with a delay between 0 and 1 hour, with all pairs of delay being equally likely. The first to arrive will wait for 15 minutes and will leave if the other has not yet arrived. What is the probability that they will meet?

Q1) Assume that the time takes you to prepare your morning coffee uniformly varies between 28...

Q1) Assume that the time takes you to prepare your morning coffee uniformly varies between 28 and 45 seconds. Calculate the following:) Probability that your next cup of coffee will take more than 35 seconds : ? Probability of getting the same cup in less than 32 seconds : ? ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Suppose the distribution is normally distributed with mean of 100 and a standard deviation of 15: What is the probability that random variable has less than 115 : ? What is the...

what do you believe about clients who have physical complaints but no demonstrated physiologic reasons for...

what do you believe about clients who have physical complaints but no demonstrated physiologic reasons for them

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives...

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives every 8 minutes starting from 7:00 am. Let Y be the waiting time. Please compute the pdf of Y.

What do you believe is a reasonable availability or utilization rate (the percentage of your time...

What do you believe is a reasonable availability or utilization rate (the percentage of your time that is charged to billable projects) is for a staff engineer one month after the engineer starts working for the company after just graduating from college? 6 Months? 1 Year? Explain the reasoning for your responses

28) You have come up with a forecast of your future earnings. You believe you will...

28) You have come up with a forecast of your future earnings. You believe you will earn: $20,000 next year (one-year from now); $40,000 two years from now; $60,000 three years from now; and, $100,000 four years from now and every year there-after for another 29 years (30 such years in total) Assume your earnings in all of these years are received as one lump-sum payment at the end of every year. Assume your personal discount rate is 8%. What...

(15) Imagine the time it takes your boss to answer your e-mails is uniformly distributed from...

(15) Imagine the time it takes your boss to answer your e-mails is uniformly distributed from 15 – 120 minutes. What is the average time it takes her to respond? What is the standard deviation for her response time? (16) What is the probability your boss will respond to an e-mail within one hour? (17) What is the probability it will take your boss longer than 30 minutes to respond? (18) What is the probability your boss will respond to...

What are some of the reasons that you believe that health insurance costs are steadily rising?

Identify the most significant reasons why you believe it is important for HR to be considered...

Identify the most significant reasons why you believe it is important for HR to be considered a strategic business partner. Also, what are the disadvantages for organizations that do not view HR as a strategic business partner? Please cite any resources you utilize.

The wait time (after a scheduled arrival time) in minutes for a train to arrive is...

The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 95 wait times you observed is between 536 and 637? Part b) What is the approximate probability (to 2 decimal places) that the average of...