You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 6 percent. If you are accepted to medical school, then your starting salary when you graduate will be $332,397 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $30,220 per year. Without considering the additional educational years or the time value of money.

Question

You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 6 percent. If you are accepted to medical school, then your starting salary when you graduate will be $332,397 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $30,220 per year. Without considering the additional educational years or the time value of money.

What is your expected starting salary?
What is the standard deviation of that starting salary?

Answer 1

To find the expected starting salary, we need to calculate the weighted average of the two possible outcomes (being accepted to medical school or working in a zoo) based on their probabilities.

Let's start by calculating the expected starting salary:

Expected Starting Salary = (Probability of being accepted to medical school x Starting salary as a medical doctor) + (Probability of not being accepted to medical school x Starting salary at a zoo)

Probability of being accepted to medical school = 6% = 0.06
Probability of not being accepted to medical school = 100% - 6% = 94% = 0.94

Starting salary as a medical doctor = $332,397 per year
Starting salary at a zoo = $30,220 per year

Expected Starting Salary = (0.06 x $332,397) + (0.94 x $30,220)
Expected Starting Salary ≈ $19,943.82 + $28,442.8
Expected Starting Salary ≈ $48,386.62

Therefore, the expected starting salary is approximately $48,386.62.

To calculate the standard deviation, we need to consider the probability and variance of each outcome.

Variance = (Probability of an outcome) x (Squared deviation from expected value)

Variance of being accepted to medical school = (0.06) x ($332,397 - $48,386.62)^2
Variance of being accepted to medical school ≈ (0.06) x ($284,010.38)^2

Variance of not being accepted to medical school = (0.94) x ($30,220 - $48,386.62)^2
Variance of not being accepted to medical school ≈ (0.94) x ($-18,166.62)^2

Now, we can calculate the standard deviation using the variance:

Standard Deviation = Square root of ((Variance of being accepted to medical school) + (Variance of not being accepted to medical school))

Standard Deviation ≈ Square root of ((0.06 x ($284,010.38)^2) + (0.94 x ($-18,166.62)^2))

Please note that since the salary difference between being accepted to medical school and not being accepted is significant, the standard deviation in this case is not as useful in providing an accurate representation of the variation in starting salaries.