csat-suneung 2018 Q26

csat-suneung · South-Korea · csat__math-science 4 marks Normal Distribution Algebraic Relationship Between Normal Parameters and Probability
A random variable $X$ follows a normal distribution with mean $m$ and standard deviation $\sigma$, and $$\mathrm { P } ( X \leq 3 ) = \mathrm { P } ( 3 \leq X \leq 80 ) = 0.3$$ Find the value of $m + \sigma$. (Here, when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 0.25 ) = 0.1 , \mathrm { P } ( 0 \leq Z \leq 0.52 ) = 0.2$ for calculation purposes.) [4 points]
A random variable $X$ follows a normal distribution with mean $m$ and standard deviation $\sigma$, and
$$\mathrm { P } ( X \leq 3 ) = \mathrm { P } ( 3 \leq X \leq 80 ) = 0.3$$
Find the value of $m + \sigma$.\\
(Here, when $Z$ is a random variable following the standard normal distribution,\\
$\mathrm { P } ( 0 \leq Z \leq 0.25 ) = 0.1 , \mathrm { P } ( 0 \leq Z \leq 0.52 ) = 0.2$ for calculation purposes.) [4 points]