Question

$X$ is a Normally distributed variable with mean $=30$ and standard deviation $=4$. Find $P(30<x<35)$

• A. $0.3698$
• B. $0.3956$
• C. $0.2134$
• D. $0.3944$

Answer 1

Answer: (D)

$0.3944$

Here we need to determine the value of $Z=\frac{x-\mu }{\sigma }$

Here, $\mu =\text{Mean}=30$ and $\sigma =\text{Stand Deviation}=4$

For, $x=30\Rightarrow Z=\frac{30-30}{4}=0$

For, $x=35\Rightarrow Z=\frac{35-30}{4}=1.25$

$\Rightarrow P(30<x<35)=P(0<Z<1.25)$

$\Rightarrow P(0<Z<1.25)=P(Z<1.25)-P(Z<0)$ $(\because P(a<Z<b)=P(Z<b)-P(Z<a\left)\right)$

From the Normal Distribution table, $P(Z<1.25)=0.8944$ and $P(Z<0)=0.5$

$\Rightarrow P(30<x<35)=0.8944-0.5=0.3944$