Question

c) What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value

Answer 1

Answer:

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Answer 2

Answer:

Suppose there are nb basaltic rocks, and ng granite rocks, and we sample nb+ng>m>max(nb,ng) rocks at random among nb+ng equiprobably. There is the total of NT=(nb+ngm) orderless configurations.

The number of configurations where k granite rocks are selected is (ngk)(nbm−k), making the probability

P(k out of m rocks are granite)=(ngk)(nbm−k)(nb+ngm)(1)

The event that all granite rocks are sampled, corresponds to event {ng out of m rocks are granite}, while the event that all basalt rocks are sampled corresponds to the event {m−nb out of m rocks are granite}. These events are disjoint, therefore

P(All specimens of one of the two types of rock are selected )=(nbm−ng)(nb+ngm)+(ngm−nb)(nb+ngm)

To answer the last question use expression (1) for pmf to compute the mean, and the standard deviation, find k that satisfy the requirement and add pmfs at those values.