Answer: 47.72 %
Step-by-step explanation:
Given : The scores of students on a statistics course are normally distributed with a mean of [tex]\mu=476[/tex] and a standard deviation of [tex]\sigma=85[/tex].
Let x be the random variable that represents the scores of students on a statistics course .
z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 476
[tex]z=\dfrac{476 -476 }{85}=0[/tex]
For x= 646
[tex]z=\dfrac{646 -476 }{85}=2[/tex]
Now, the probability of the students scored between 476 and 646 on the exam will be :-
[tex]P(476<X<646)=P(0<z<2)=\\\\P(z<2)-P(z<0)= 0.9772498-0.5= 0.4772498\approx47.72\%[/tex]
Hence, the percentage of the students scored between 476 and 646 on the exam = 47.72 %
