Answer: 0.9575465
Step-by-step explanation:
Let the random variable X is normally distributed with mean [tex]\mu=50[/tex] and standard deviation[tex]\sigma=7[/tex] .
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex] , we have the z-value for x= 34
[tex]z=\dfrac{34-50}{7}\approx-2.29[/tex]
For x= 63
[tex]z=\dfrac{63-50}{7}\approx1.86[/tex]
P-value : P(34<x<63)=P(-2.29<z<1.86)
[tex]=P(z<1.86)-P(z<-2.29)\\\\=0.9685572-(1-P(z<2.29))\\\\1=0.9685572-(1-0.9889893)\\\\=0.9575465[/tex]
Hence, the required probability = 0.9575465
