131 132 133 134 135 giúp em vs ạ 😪

Câu 131:

Gọi $X$ là chiều cao của giống cây trồng

$\Rightarrow X$ có phân phối chuẩn: $X\sim\mathscr{N}(21,38;34,27)$

Tỉ lệ cây có chiều cao không dưới $20\ m:$

$\quad P(X \geqslant 20) = \dfrac12 - \varphi\left(\dfrac{20 - 21,38}{\sqrt{34,27}}\right)$

$\Leftrightarrow P(X \geqslant 20) = \dfrac12 + \varphi(0,24)$

$\Leftrightarrow P(X \geqslant 20) = 0,5 + 0,0948$

$\Leftrightarrow P(X \geqslant 20) = 0,5948$

Câu 132:

$X\sim\mathscr{N}(a;0,25)$

Ta có:

$\quad P(X > 12) = 0,34$

$\Leftrightarrow \dfrac12 - \varphi\left(\dfrac{12 - a}{0,5}\right) = 0,34$

$\Leftrightarrow \varphi\left(\dfrac{12 - a}{0,5}\right) = 0,16$

$\Leftrightarrow \dfrac{12 - a}{0,5} = 0,42$

$\Leftrightarrow a = 11,79$

Câu 133:

$X\sim\mathscr{N}(3,2;\sigma^2)$

Ta có:

$\quad P(X >5) = 0,025$

$\Leftrightarrow \dfrac12 - \varphi\left(\dfrac{5 - 3,2}{\sigma}\right) = 0,025$

$\Leftrightarrow \varphi\left(\dfrac{5 - 3,2}{\sigma}\right) = 0,475$

$\Leftrightarrow \dfrac{1,8}{\sigma} = 1,96$

$\Leftrightarrow \sigma \approx 0,92$

Câu 134:

$X\sim\mathscr{N}(0;1)$

Ta có:

$\quad P(0 < X < a) = 21,57\%$

$\Leftrightarrow \varphi(a) - \varphi(0) = 0,2157$

$\Leftrightarrow \varphi(a) = 0,2157$

$\Leftrightarrow a = \varphi^{-1}(0,2157)$

$\Leftrightarrow a = 0,57$

Câu 135:

$X\sim \mathscr{P}(3) \Rightarrow E(X) = \lambda = 3$

$Y\sim \mathscr{N}(4;1,21) \Rightarrow E(Y) = \mu = 4$

$Z \sim\mathscr{B}(12;0,8) \Rightarrow E(Z) =np = 9,6$

Khi đó:

$\quad T = 3XY - 2Z + 2010$

$\Rightarrow E(T) = E(3XY - 2Z + 2010)$

$\Leftrightarrow E(T) = 3E(X).E(Y) - 2E(Z) + 2010\quad (X,Y,Z$ độc lập$)$

$\Leftrightarrow E(T) = 3\cdot 3\cdot 4 - 2\cdot 9,6 + 2010$

$\Leftrightarrow E(T) = 2026,8$