Question

X is normally distributed.The mean of X is 15 and S.D is 3 . Given that for z=1,A=0.3413 ,p(X>=18) is given by​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{X is normally distributed with mean 15 and}$

$\textsf{standard deviation 3}$

$\underline{\textbf{To find:}}$

$\mathsf{P(X\,\geq\,18)}$

$\underline{\textbf{Solution:}}$

$\textsf{Standard normal variable,}\;\mathsf{z=\dfrac{X-mean}{S.D}}$

$\mathsf{When\;X=18,\;\;z=\dfrac{X-mean}{S.D}=\dfrac{18-15}{3}=1}$

$\mathsf{Now,}$

$\mathsf{P(X\,\geq\,18)}$

$\mathsf{=P(z\,\geq\,1)}$

$\mathsf{=P(0\,<\,z\,<\,\infty)-P(0\,<\,z\,<\,1)}$

$\mathsf{=0.5-0.3413}$

$\mathsf{=0.1587}$

$\implies\boxed{\mathsf{P(X\,\geq\,18)=0.1587}}$