Question

(1 point) A geologist has collected 10 specimens of basaltic rock and 12 specimens of granite. The geologist instructs a laboratory assistant to randomly select 17 of the specimens for analysis. (a) What is the probability that all specimens of one of the two types of rock are selected for analysis? Probability (b) What is the expected value and the standard deviation of the number of granite specimens selected for analysis? Mean= Standard Deviation= (c) What is the probability that the number of granite specimens selected for analysis is withing 1 standard deviation of its mean value? Probability=

Answer 1

here this is hypergeometric distribution with parameter:
sample size n=	17
population N=	22
success size k=	12

a)

probability =P(all 10 basaltic and 7 granite)+P(5 basaltic and all 12 granite)

=(₁₀C₁₀)*(₁₂C₇)/(₂₂C₁₇)+(₁₀C₅)*(₁₂C₁₂)/(₂₂C₁₇) =0.0301+0.0096 =0.0396

b)

mean μ=nk/N =

9.2727

std deviation σ=√((nk/N)*(1-k/N)*(N-n)/(N-1)) =

1.0018

c)

1 standard deviation from mean values are μ -/+ 1*σ=(8.27,10.27)

P(9<=X<=10)=

∑x=ab (kCx)(N-kCn-x)/(NCn) =

0.6767