maduregimc
2022-01-14
ol3i4c5s4hr
Beginner2022-01-15Added 48 answers
Given Information:
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite.
15 of the specimens are selected for analysis.
(a) To find the PMF of the number of granite specimens selected for analysis:
Let X denote the number of granite specimens selected for analysis. In order to have less than 5 of the granite, there would have to be more than 10 of the basaltic rock.
Possible values of X are: 5, 6, 7, 8, 9, 10.
X follows hyper geometric distribution.
Formula:
where, M=10, N=20, n=15 and r=5,6....10 For r = 5:
For r = 6:
For r = 7:
Similarly, Calculating the other values of r, we get the PMF in table form, which is given below:
Debbie Moore
Beginner2022-01-16Added 43 answers
(b) To find the probability that all specimens of one of the two types of rock are selected for analysis:
Required probability is obtained as follows:
P(all 10 of one kind OR the other)
=P(X=5)+P(X=10)
=0.0163+0.0163
=0.0326
[if all 10 of basaltic are selected i.e., X = 5, whereas X = 10 means all 10 of the granite are selected]
Thus, the probability that all specimens of one of the two types of rock are selected for analysis is 0.0326
(c) To find the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value:
Mean of Hypergeometric distribution is calculated as follows:
Variance is calculated as follows:
Standard deviation is obtained by taking the square root of variance:
Within 1 standard deviation:
Required probability is obtained as follows:
Thus, probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is 0.6966
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