Answer: A. 103
Step-by-step explanation:
Given : The final exam scores in freshman English at a large high school are normally distributed with a mean of 84% and a standard deviation of 14%.
i.e. [tex]\mu=84\%[/tex] and [tex]\sigma=14\%[/tex]
Let x be the exam scores in freshman English ( in percent ).
Then, the probability that students scored between 70% and 80% would be
[tex]P(70<x<80) =P(\dfrac{70-84}{14}<\dfrac{x-\mu}{\sigma}<\dfrac{80-84}{14})\\\\=P(-1<z<-0.2875)\ \ [\beacuse \ z=\dfrac{x-\mu}{\sigma}]\\\\=P(z<-0.2875)-P(z<-1)\\\\=(1-P(z<0.2875))-(1-P(x<1))\ \ [\because P(Z<-z)=1-P(Z<z)]\\\\=P(z<1)-P(z<0.2875)\\\\= 0.8413-0.6124=0.2289\ \ [\text{By z-table}][/tex]
If 450 students took the exam, then the number of students scored between 70% and 80% = 450 x ( probability that students scored between 70% and 80%)
= 450 x 0.2289=103.005≈ 103
Therefore , About 103 students scored between 70% and 80% .
Hence, the correct answer is A. 103 .