select the correct answer. laura is looking for a way to save money this year on her medical expenses…

select the correct answer. laura is looking for a way to save money this year on her medical expenses. insurance is starting to get expensive, and her budget is tight. she figures that she has a 75% chance of needing to visit the doctor and get medication once in the winter, for a total of about $400. she also figures there should be some room in the budget for emergencies, so she estimates a 5% chance she will need to spend $300 at an emergency room. is it reasonable for laura to set her medical budget at $300 for the year? a. no. the expected value is over $300, so laura will likely need more money to cover her expenses. b. no. the sum of the possible expenses is $700, so she should budget exactly that amount. c. yes. as long as laura has $300 for emergencies, she will likely have enough to cover any expenses. d. yes. the expected value is under $300, so laura will likely have enough money to cover her expenses.

select the correct answer. laura is looking for a way to save money this year on her medical expenses. insurance is starting to get expensive, and her budget is tight. she figures that she has a 75% chance of needing to visit the doctor and get medication once in the winter, for a total of about $400. she also figures there should be some room in the budget for emergencies, so she estimates a 5% chance she will need to spend $300 at an emergency room. is it reasonable for laura to set her medical budget at $300 for the year? a. no. the expected value is over $300, so laura will likely need more money to cover her expenses. b. no. the sum of the possible expenses is $700, so she should budget exactly that amount. c. yes. as long as laura has $300 for emergencies, she will likely have enough to cover any expenses. d. yes. the expected value is under $300, so laura will likely have enough money to cover her expenses.

Answer

Explanation:

Step1: Calculate the expected value

The expected - value formula for a discrete random variable is (E(X)=\sum_{i}x_ip_i). Here, we have two scenarios:

  1. With a probability (p_1 = 0.75), the expense is (x_1 = 0) (no need to visit the doctor and get medication).
  2. With a probability (p_2=0.05), the expense is (x_2 = 400) (doctor - visit and medication).
  3. With a probability (p_3 = 0.2) (since (1-(0.75 + 0.05)=0.2)), the expense is (x_3 = 300) (emergency room visit). [E(X)=0\times0.75 + 400\times0.05+300\times0.2] [E(X)=0 + 20+60] [E(X)=80]

Since the expected value (E(X) = 80) is well under the budget of (300), it is reasonable for Laura to set her medical budget at (300) for the year.

Answer:

D. Yes. The expected value is under $300, so Laura will likely have enough money to cover her expenses.