Question

53. The Mean and SD for a, b and 2 are 3 and 1
respectively. Then the value of ab would be (€)
a) 5 b) 6 c) 11.5 d) 3​

Answer 1

Answer:

Mean of a,b and 2 =( a+b+2)/3 =3, a+b = 7 therefore b = 7-a

SD of a, b and 2

= √[ {(a-3)^2 + (b-3)^2 + (2–3)^2}/3] =2/√3

=> √[ a^2 -6a+9 +1+(7-a -3)^2] =2

=> √[ a^2 -6a +9 +1+ 16–8a+a^2]=2

=> 2a^2 -14a +26=4 , 2a^2–14a+22=0

=> a^2 -7a +11=0, a = (7±√5)/2,

So, b=7-(7±√5)/2 = (7 -(+)√5)/2

It is clear that if a = (7+√5)/2 , b= (7-√5)/2, ab = (49–5)/4 =11

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