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

Solution

The correct option is C $$0.3944$$Here we need to determine the value of $$Z=\dfrac{x-\mu}{\sigma}$$Here, $$\mu=\text{Mean}=30$$ and $$\sigma=\text{Stand Deviation}=4$$For, $$x=30\Rightarrow Z=\dfrac{30-30}{4}=0$$For, $$x=35\Rightarrow Z=\dfrac{35-30}{4}=1.25$$$$\Rightarrow P(30<x<35)=P(0<Z<1.25)$$$$\Rightarrow P(0<Z<1.25)=P(Z<1.25)-P(Z<0)$$                         $$(\because P(a<Z<b)=P(Z<b)-P(Z<a))$$From the Normal Distribution table, $$P(Z<1.25)=0.8944$$ and $$P(Z<0)=0.5$$$$\Rightarrow P(30<x<35)=0.8944-0.5=0.3944$$Maths

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