an a act on cs store has rece veashipment of 25 table ados that have connections

Question

an a act on cs store has rece veashipment of 25 table ados that have connections or an Pod cr phone. Ten of these have twn sots so they can accom nadate both devices wher-the rartins are displavad, ard tha ramaining res are planed in a terernnm. I et X-me nirmher among rados sterert under th tsplay Sher that haVA tan slots. ana the ot er een hava a snq e slot. SuppcG2 t at stx cf e 25 rad ns are randomly selected tn be stoned under a shelf (a) What kind af distribution daas X have (nama and values at all parameters)? hypergeometric with N-25, M-10, and n-6 binomial with -25, x. 10, and O-6/25 o binomial with-10,x-6, and p-6/10 s hrpergeometrik with W- 10, -6, andn-10 (b) compute (X-2), s 2), and p2 2). (Round ur ariswers to four decimal places.) (C) Calculate the mean value and standard deviation of Round your standard deviation to two decimal places.) standerd desiatio

Explanation / Answer

(a) hypergeometric N=25, M=10 and n=6

P(X=m)=MCmN-MCn-m/NCn

(b) P(X=2)=10C225-10C6-2/25C6=10C215C4/25C6=(45*1365)177100=0.3468

P(X<=2)=P(X=0)+P(X=1)+P(X=2)=0.0283+0.1696+0.3468=0.5447

P(X>=2)=1-P(X<2)=1-P(X=0)-P(X=1)=1-0.0283-0.1696=0.8021

(c) mean=n*M/N=6*10/25=2.4

variance==n*M*(N-M)*(N-n)/(N*N*(N-1))=6*10*(25-10)*(25-6)/(25*25*(25-1)=1.14

standard deviation=sqrt(1.14)=1.07

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