Answer: A. 103
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.
and

Let x be the exam scores in freshman English ( in percent ).
Then, the probability that students scored between 70% and 80% would be
![P(70<x<80) =P((70-84)/(14)<(x-\mu)/(\sigma)<(80-84)/(14))\\\\=P(-1<z<-0.2875)\ \ [\beacuse \ z=(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}]](https://img.qammunity.org/2021/formulas/mathematics/college/hqlg4ozpeds0z7kuaryho5nmhnucrec0i0.png)
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 .