For questions 1-3, suppose that you are considering whether to invest in a new b

Question

For questions 1-3, suppose that you are considering whether to invest in a new business that a fiend of yours is starting. After researching the possibälities, you decide that you will $40,000if the busines is succesfiå, and yol l00 the business is not successial gain 1. Suppose that 30% ofall such businesses are successful, so you consider to be the probability that your friend's business will be successful. Determine the expected value of your net profit. (Here and always, show your method of solution.) 2. Write a sentence interpreting/explaining what this expected value means, as if to a college student who has never taken a probability and statistics class 3. If you decide to invest in your friend's business, what is the probability that your net profit will exceed its expected value?

Explanation / Answer

1:

Let X is a random variable shows your profit. So, X can take values 40000 and -10000.

(a)

The probability og success is 0.3 so

P(X = 40000) = 0.3

P(X = - 10000) = 1-0.3 = 0.7

The expected valeu of your net profit is

E(X) = 40000 * P(X=40000) + (-10000) * P(X= -10000) = 40000 * 0.3 + (-10000) * 0.7 = $5000

2:

It shows that in the long run your profit will be $5000 if you will invest in the business.

3:

Expected value shows the mean of the distributed. SO there will be 50% chance that your profit will exceed from expected value.

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