\[\begin{array}{1 1}(1)120&(2)20\\(3)80&(4)160\end{array}\]

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Let X denotes the marks secured.

$\mu=65$

$X \sim N (65, \sigma)$

$Z =\large\frac{X-\mu}{\sigma} =\frac{X- 65}{\sigma}$

$P (X > 85) =\large\frac{120}{400}$

$P \bigg( Z > \large\frac{85-65}{\sigma} \bigg)= \frac{3}{10}$

$P \bigg( Z > \large\frac{20}{\sigma} \bigg)= \frac{3}{10}$-------(1)

$P (45 K< x< 65)$

$\qquad= P\bigg( \large\frac{45-65}{\sigma} < z < \large\frac{65-65}{\sigma}\bigg)$

$\qquad= P \bigg( -\large\frac{20}{\sigma} < z <0 \bigg)$

$\qquad= P \bigg(0 < z < \large\frac{20}{\sigma} \bigg)$

$\qquad =0.5 -P \bigg(z > \large\frac{20}{\sigma } \bigg)$

$\qquad= \large\frac{1}{2} -\frac{3}{10} $

$\qquad= \large\frac{5-3}{10} =\frac{2}{10} =\frac{1}{5}$

Number of student secured marks between 45 and 65 $ =\large\frac{1}{5} \times$$ 400$

$\qquad=80$

Hence 3 is the correct answer.

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