Answer: 0.9834
Step-by-step explanation:
Given : The test scores are normally distributed with
Mean : [tex]\mu=\ 0[/tex]
Standard deviation :[tex]\sigma= 1[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = -2.13
[tex]z=\dfrac{-2.13-0}{1}=-2.13[/tex]
For x = 3.88
[tex]z=\dfrac{3.88-0}{1}=3.88[/tex]
The p-value = [tex]P(-2.13<z<3.88)=P(z<3.88)-P(z<-2.13)[/tex]
[tex]0.9999477-0.0165858=0.9833619\approx0.9834[/tex]
Hence, the probability that a given score is between negative 2.13 and 3.88 = 0.9834
