Question

Azzalini and Bowman (1990) analyzed the data of the waiting time (in minutes) of consecutive eruptions of the Old Faithful geyser in Yellowstone National Park. They found that the waiting times can be categorized into two groups in historical data.

-In group 1, waiting time is normally distributed with mean 54 minutes and standard deviation of 2.95.

-In group 2, the waiting time is normally distributed with mean 80 minutes and standard deviation of 7.5.

Suppose that there is a 30% chance that the waiting time is from group 1. They want to simulate the waiting time.

a) Use Excel functions only to simulate the waiting time. Your simulations should contain 500 iterations. you need only to return in one page showing your model and one page displaying the formulas in your model.

b) what is the average waiting time in your simulation?

Answer 1

I am using the following formula to simulate values. The following is an excel function. The random numbers by default range only from [0,1]

IF(RAND()<0.3,NORM.INV(RAND(),54,2.95),NORM.INV(RAND(),80,7.5))

Let me explain the formula, We are generating a random number and see if the value is less than or greater than 0.3

If the value is less than 0.3, we would generate a waiting time from group 1. This would be done using an inverse normal probability function.

Again if the value is greater than 0.3, we would generate a waiting time from group 2.

Like this we generate 500 random numbers. I have attached a screenshot of the same.

To calculate the average i have used formula->AVERAGE(A1:T25)=71.79

Theoretically, we need to get the average value approximately as 0.3*54+0.7*80=72.2. So, the simulation provided a result close to it.