Question

Your health insurance company has converge for three types of medical treatment. The annual cost for each type of treatment can be modeled using Gaussian (Normal) distribution, with the following parameters:

• Treatment 1: Mean=$1600 and Standard Deviation=$120
• Treatment 2: Mean=$1500 and Standard Deviation=$95
• Treatment 3: Mean=$1200 and Standard Deviation=$70

Use Random number generator and simulate 1000 long columns, for each of the three cases.
Example: for the Treatment 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=1600 and Standard deviation=120, and leave random Seed empty.
Next: use either sorting or construct the appropriate histogram or rule of thumb to answer the questions:

23. What is approximate probability that Treatment 3 has annual cost less than $1150? (4 points)

• a. Between 20% and 30%
• b. Between 30% and 70%
• c. Between 70% and 85%
• d. None of these

24. Which of the three treatment is most likely to cost between $1200 and $1300? (4 points)

• a. Treatment 1
• b. Treatment 2
• c. Treatment 3

25. For which of the three treatments we expect that (approximately) 95% of cases will be between $1300 and $1700? (4 points)

• a. Treatment 1
• b. Treatment 2
• c. Treatment 3

Answer 1

23. What is approximate probability that Treatment 3 has annual cost less than $1150? (4 points)

p(X<$1150) =0.23

• a. Between 20% and 30%

24. Which of the three treatment is most likely to cost between $1200 and $1300? (4 points)

p(1200<X<1330) for T1=0.005

For T2=0.01

for T3=0.42

Hence treatment3 is most likely to cost between $1200 and $1300

25. For which of the three treatments we expect that (approximately) 95% of cases will be between $1300 and $1700? (4 points)

b. Treatment 2

p(1300<X<1700) for T1=0.79

For T2=0.96

For T3=0.076

Hence Answer is b. Treatment 2