A geologist has collected 17 specimens of basaltic rock and 17 specimens of granite. The geologist instructs a laboratory assistant to rando

Question

A geologist has collected 17 specimens of basaltic rock and 17 specimens of granite. The geologist instructs a laboratory assistant to randomly select 29 of the specimens for analysis.

a. What is the pmf of the number of granite specimens selected for analysis?
b. What is the probability that all specimens of one of the two types of rock are selected for analysis?
c. What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value?

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Aaliyah 4 days 2021-10-10T03:43:51+00:00 1 Answer 0

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    2021-10-10T03:45:37+00:00

    Answer:

    Step-by-step explanation:

    Out of N = 34specimens, K = 17 are granite and 17 are basaltic.

    Let X be the number of specimens that are granite in randomly selected n = 29 specimens

    Tthe geometric random variable  can only take integer values  in range ; [max ( 0 , n + K – N), min (n, K )] = [ 12, 17] using the combination method;

    nCr = n!/(n – r) r)! which is as shown below.

    a)

    X P(X)

    12 0.0222

    13 0.1454

    14 0.3324

    15 0.3324

    16 0.1454

    17 0.0222

    b) P (all specimens of one of the two types of rock are selected for analysis

    = C(17,17) x C (17,12) / C34,29) + C(17,12) x C (17,17) / C34,29) = 0.0445

     

    c) Sample size, n =    29

    • No. of events of interest in population , k =   17
    • Population size  , N = 34
    • mean = E(X) = n(k/N) = 14.5
    • variance = nk(N-k)(N-n)/(N²(N-1)) = 1.0985

    Therefore, the probability that the number of granite specimens selected is within 1 standard deviation of mean ;

    P (µ-σ < X < µ+σ) = P(14.5-1.05 < X <14.5+1.05) = P(13.45 < X <15.55) = P(X=14) + P(X=15) = 0.3324 + 0.3324 = 0.6647

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