Question

Sendo X~N(15,9), assinale a alternativa que contém o valor de P(12 < X < 18).
a) 15,9%
b) 84,1%
c) 62,8%
d) 42,9%
e) 68,2%

Alguém sabe como faz o calculo?

Answer 1

Boa tarde Claudia!

Solução!

Para você resolver esse tipo de exercício de distribuição normal,basta usar essa formula e uma tabela de distribuição em z.

$z= \dfrac{x-\mu}{\sqrt{\sigma}}\\\\\\\ \mu=media\\\\\\\ \sigma=desvio~~padr\~ao\\\\\\\ N^{~} (15,9)\\\\\\\ P(12\ \textless \ x\ \textless \ 18)$


$P(x\ \textless \ 18)=1-P(x\ \textless \ 18)\\\\\ Z= \dfrac{18-15}{ \sqrt{9} }\\\\\\\ Z= \dfrac{3}{3}\\\\\ \boxed{Z=1}\\\\\\ Na~~tabela~!~~1=0,841$

$P(x\ \textless \ 12)= \dfrac{12-15}{ \sqrt{9} }\\\\\\\ P(x\ \textless \ 12)= \dfrac{-3}{3} \\\\\\\\ P(x\ \textless \ 12)=-1~~Na~~tabela~~-1=0,159\%\\\\\\\\\\ P(12\ \textless \ x\ \textless \ 18=0,841-0,159\\\\\\ P(12\ \textless \ x\ \textless \ 18)=0,682\\\\\\\ P(12\ \textless \ x\ \textless \ 18)=0,682\times 100\\\\\\ P(12\ \textless \ x\ \textless \ 18)=68,2$



$\boxed {Resposta~~\boxed{P(12<x\ \textless \ 18)=68,2\%} ~~\boxed{Alternativa~~E}}$

Answer 2

A alternativa correta é 68,2%