Let X denote the mean of a random sample of size 25 from a gamma-type distribution with α = 4 and β > 0. Use the Central Limit Theorem to find an approximate 0.9544 confidence interval for β, the mean of the gamma distribution. Hint: Use the random variable (X − 4β)/ p 4β 2/25 = 5X/2β − 10.

Two farmers pay a total rent of $140 for a pasture. the first farmer placed $4 oxen in the pasture, and the second farmer placed $30 sheep in the pasture. the farmers split the rent based on the proportion of the pasture eaten by their own animals that month. how much should the first farmer pay, if 1 ox eats as much as 10 sheep in a month?