A geologist collected 5 specimens of limestone rock and 5 specimens of sandstone. A lab assistant...

A geologist collected 5 specimens of limestone rock and 5 specimens of sandstone. A lab assistant randomly selects 7 specimens for analysis. Let X = the number of sandstone samples that are selected.

a) What is the name of the distribution of X?

b) What is the probability that all specimens of one of the two types of rock are selected?

c) What is the probability that the number of sandstone specimens selected is within 1 standard deviation of its mean value?

Expert Solution

a.

X follows hypergeometric distribution with parameter N = 10, K = 5 and n = 7

Thus pmf of X is

b.

Probability that all specimens of one of the two types of rock are selected is zero. Because X take values from 2 to 5. For remaining values, probability is zero.

Logically, see there are only 5 specimens of sandstone and we have to select 7 specimens of sandstone, which is not possible. Hence probability of this event is zero.

c.

According to emperical rule, the probability that the number of sandstone specimens selected is within 1 standard deviation of its mean value is 0.68

orchestra answered 2 years ago

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