Question

If x is a normal variate with mean 5 and standard deviation 4. Find P(4<x<9)​

Answer 1

0.3944

Here we need to determine the value of Z=

σ

x−μ

Here, μ=Mean=30 and σ=Stand Deviation=4

For, x=30⇒Z=

4

30−30

=0

For, x=35⇒Z=

4

35−30

=1.25

⇒P(30<x<35)=P(0<Z<1.25)

⇒P(0<Z<1.25)=P(Z<1.25)−P(Z<0) (∵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

⇒P(30<x<35)=0.8944−0.5=0.3944