The mineral museum in Butte, MT is interested in selling bags of rocks containing a mix of geodes and nodules for customers to crack open. Suppose they have 350 nodules and 250 geodes to randomly draw 12 rocks from with which to make these bags. Let X be the number of geodes in a bag.

mineral museum in Butte, MT is interested in selling bags of rocks containing a mix of geodes and

1. What distribution does X follow? Include the parameters for the identified distribution in proper notation.
2. How many geodes can be expected in any given bag? What is the variance of the number of geodes in a bag?
3. Calculate the probability that exactly half of the rocks in a randomly selected bag are geodes.
4. Calculate the probability that more than one third of the rocks in a randomly selected bag are geodes.