Answer: 0.1498 square units.
Step-by-step explanation:
Let x be any random variable that follows normal distribution.
Given : For a normal distribution with mean equal to - 30 and standard deviation equal to 9.
i.e. [tex]\mu=-30[/tex] and [tex]\sigma=9[/tex]
Use formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex] to find the z-value corresponds to -34.5 will be
[tex]z=\dfrac{-34.5-(-30)}{9}=\dfrac{-34.5+30}{9}=\dfrac{-4.5}{9}=-0.5[/tex]
Similarly, the z-value corresponds to -38 will be
[tex]z=\dfrac{-39-(-30)}{9}=\dfrac{-39+30}{9}=\dfrac{-9}{9}=-1[/tex]
By using the standard normal table for z-values , we have
The area under the curve that is between - 34.5 and - 39. will be :-
[tex]P(-1<z<-0.5)=P(z<-0.5)-P(z<-1)\\\\=(1-P(z<0.5))-(1-P(z<1))\\\\=1-P(z<0.5)-1+P(z<1)\\\\=P(z<1)-P(z<0.5)\\\\=0.8413-0.6915=0.1498[/tex]
Hence, the area under the curve that is between - 34.5 and - 39 = 0.1498 square units.
