Questions: Question Part 1 of 5 The Carbonate Hospital is considering the purchase of a new ambulance. The decision will rest partly on the annual mileage to be driven and will be based on 6 years of data. Using a 2-year moving average, the forecast for year 6 is miles. Round your response to the nearest whole number. Year Mileage 1 3,000 2 4,000 3 5,500 4 3,000 5 3,000

Solution Steps

The annual mileage data for the first five years is as follows:

• Year 1: \(3000\) miles
• Year 2: \(4000\) miles
• Year 3: \(5500\) miles
• Year 4: \(3000\) miles
• Year 5: \(3000\) miles

To forecast the mileage for year 6, we use a 2-year moving average. This is calculated using the mileage from years 4 and 5.

The formula for the mean is given by: \[ \mu = \frac{\sum_{i=1}^N x_i}{N} \] where \(N\) is the number of data points.

For years 4 and 5: \[ \mu = \frac{3000 + 3000}{2} = \frac{6000}{2} = 3000.0 \]

The forecasted mileage for year 6, based on the 2-year moving average, is: \[ \text{Forecast for Year 6} = 3000.0 \text{ miles} \]

Final Answer