Final answer:
The provided linear regression model can be used to make sales predictions, and the probability of a traveler purchasing an airline ticket fewer than 10 days in advance can be calculated using the exponential probability density function with a mean of 15 days.
Step-by-step explanation:
The question pertains to generating forecasts using exponential smoothing, which is a technique used in time series analysis to produce smoothed data point values. However, the actual data required to calculate the forecasts for periods 11 through 15 using exponential smoothing is not provided, thus preventing the calculation. Exponential smoothing employs a smoothing constant α, which is given as 0.60 in this case, to weigh the most recent observation differently from past observations. Without the prior data or an initial forecast value, the forecast for the future periods cannot be accurately computed.
For the regression model question, on day 60, the predicted sales would be calculated using the given linear regression model ŷ = 101.32 + 2.48x. Inserting x = 60, the sales prediction would be ŷ = 101.32 + (2.48 × 60) ≈ 249.72 thousand dollars.
The same method would be applied for day 90: ŷ = 101.32 + (2.48 × 90) ≈ 324.92 thousand dollars.
The subject of probability with exponential distribution as in the airline ticket purchase scenario, where a traveler is likely to purchase a ticket fewer than 10 days in advance, would require use of the exponential probability density function:
β = 1/mean = 1/15
P(X < x) = 1 - e^{-βx}
Substituting x with 10, P(X < 10) = 1 - e^{-10/15} ≈ 0.4866, which is approximately 48.66% probability.