Losses are assumed to have an exponential distribution with unknown mean [math]\theta[/math]. Ten policies have a deductible of $500 and the total number of non-zero payments for the ten policies has the moment generating function

[[math]] (0.2 + 0.8e^t)^{10} [[/math]]

Determine which interval contains the mean [math]\theta[/math].

• [100, 150]
• [300, 320]
• [475, 525]
• [1750, 2000]
• [2200, 2400]