Question

20% of individuals participating in a study possess Gene A. On a particular day, what is the probability that, out of 10 individuals participating, 2 of them do not possess the Gene A? What is the probability that the number of individuals participating with Gene A will be within 0.3 of the true population mean? How many individuals must participate to have the probability of at least one Gene A individual over 0.80?

Answer 1

g) Ruobability that out of 10 people Panticipating , a do not possess bene Ais computed chere as: Probability that 8 of the 10 Individuals possess gene A P(x =8) (39) 0.20 (1-0-2) ?= 0.000074 Therefore 0.000074 is the required probability here. 2 b) The tame population mean chare ? computed chane asi Mean = np= 0.2 x 10=2 Therefore the probability here is computed as P(2-0-3<x<2 +0.3) -o-3)=P(x=2) = (102) xo. 2²x (1-0-28 = 0.3020 Therefore 0-3020 Ps the required probability here. e for a sample size of n the probabilite of having atleast one individual with gene A would be compected as:

Del = 1- Probability of no one with gone A = 1-(1-0.2)h I-Oogų ce Therefore we have chane 1-oogh og ognço.2 Taking natural log both sides, we have cheue neog 0,8 = log (0.2) n= log (0.2) = 7.2 log (org) Therefane & is the minimum sample sized Mona

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