Question

You are trying to decide whether or not to book a cheap flight to fly home from NCSU after your final exams, but you're not sure when your last exam will be. You think there is a 30% chance that your last exam will be scheduled after the last day that you can get a seat on the cheap flight. If it turns out that your last exam is scheduled after the last day that you can get a seat on the cheap flight, then you will have to cancel the flight, resulting in a loss to you of $150. If you can take the cheap flight home you will save $100. Question 1. If you book the cheap flight, what is your expected gain? ____ dollars.Question 2. If you book the cheap flight, what is the standard deviation of your gain? _____ dollars.

Answer 1

Answer:

Expected gain $25

Standard deviation of the gain $134.63

Step-by-step explanation:

Let C, T the events

C = You have to cancel the flight

T = You can take the flight

P(C) = 30% = 0.3 with a “gain” of -$150

P(T) = 70% = 07  with a gain of $100

Expected gain E

E = -150P(C) + 100P(T) = -150*0.3 + 100*0.7 = -45 + 70 =$25

Standard deviation of your gain

$\large\bf \sqrt{\frac{(-150-E)^2+(100-E)^2}{2}}=\sqrt{\frac{(-150-25)^2+(100-25)^2}{2}}=\\\\=\sqrt{18125}= 134.63$

Answer 2

Using the discrete distribution, it is found that:

1. The expected gain is of 25 dollars.

2. The standard deviation is of 114.56 dollars.

What are the mean and the standard deviation of a discrete distribution?

• The mean is given by the sum of each outcome multiplied by it's probability.

• The standard deviation is given by square root of the sum of the difference squared of each outcome and the mean, multiplied by it's respective probability.

In this problem, considering the scenarios, the distribution is:

P(X = -150) = 0.3

P(X = 100) = 0.7

Hence:

$E(X) = 0.3(-150) + 0.7(100) = 25$

$\sqrt{V(X)} = \sqrt{0.3(-150-25)^2 + 0.7(100-25)^2} = 114.56$

1. The expected gain is of 25 dollars.

2. The standard deviation is of 114.56 dollars.

More can be learned about the mean and the standard deviation of a discrete distribution at https://brainly.com/question/24855677