Question

a data set of 90 observations has a mean of 50 and standard deviation of 10

ESLIun 14 A data set of 90 observations has a mean of 50 and standard deviation of 10. Which of the following is not necessarily true "The interval (20,80) has at least 80 observations" "The interval (40,60) contains approximately 68% of the observations" "The interval (30,70) has at least 75% of the observations" Impossible to know A Moving to another question will save this response.

Answer 1

So answer is Option B, which is not necessarily true.

We have the Tcheby sher's in equality Pluto < X < Ma to ] = 1 - 1 / 2 @ (20,80) here M=50 ie, t=3 5 = to 2 11=90 32 atleast 80 p[ 50-3610 < x < 50+ 3+10)=P [ 201x280) 2 1 - 1 21- is, (220, 80) unterval contains & % of Observatwns ies 404 90 is 79.992 2 80 ve (20,80) interveel contains atlast do Obsesuatwns true ② (30,70) ię P (50 - 2*10 < x2 50 +2 +10] 21-1 ie, t= 2 Pl 30<x<ro ] =1-1 ? 314 ie (30,70) contains alteast 2 of to observations ie (30, 20) contains atleast 75 t of observations true b) using inequality we can only say a lowes bound not a approximare percentage , so Ibis false 22

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