Write the name of the distribution that correctly models the following scenarios

Question

Write the name of the distribution that correctly models the following scenarios (2 pts each) A pet store has a large tank with fish that are available to be sold individually (you can buy one fish at a time, you don't have to buy the whole tank). When a child comes to the store to buy a fish, he is shown one fish at a time until he finds one he likes to take home. Each fish has an 85% chance of being liked and purchased by a child. How many fish will the child see before he buys one? a. b. A factory has 10 stamping machines in operation. Each machine has an independent 10% chance of failing and requiring maintenance each day, what is the probability that 4 machines need maintenance today?

Explanation / Answer

a)

here as the experiment continues til desired event occrus; also probability of desired event is fixed and independnet from event to event

therefore this is geometric distribution with paramter p=0.85

b)

here probability of success is fixed and independnet from event to event

also number of trails are fixed therefore this follows binomial distribution with parametr p=0.10 and n=10

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