Question

A = {x € N : 1 < x <17}
B = {ax + b : x € A@} a > 0
Variance of set B is 216 and mean is 17 find a+ b?
-7
7
6
-6 ​

Answer 1

it has given that, A = {x ⊆ N : 1 ≤ x ≤ 17}

B = {ax + b : x ⊆ A } a ≥ 0

variance of set B is 216 and mean is 17.

To find : The value of (a + b)

solution : now, B( mean of x) = a(mean of x) + b = 17

⇒a(1 + 2 + 3 + ..... + 17)/17 + b = 17

⇒a (17 × 18/17 × 2) + b = 17

⇒9a + b = 17 ........(1)

again, variance of x , σ² = $\frac{\Sigma x^2}{N}-(\bar x)^2$

= (1² + 2² + 3² + .. + 17²)/17 - 9²

= 17 × 18 × 35/17 × 6 - 81

= 105 - 81

= 24

we know, Var(B) = Var(ax + b) = a² Var(x)

so, 216 = a² × 24

⇒a² = 9

⇒a = 3

so, b = -10

now the value of a + b = 3 - 10 = -7