$A$ beam of white light falling on a glass prism gets split up into seven colours marked $1$ to $7$ as shown in the diagram. $A$ student makes the following statements about the spectrum observed on the screen.
$(a)$ The colours at position marked $3$ and $5$ are similar to the colour of the core of a hard-boiled egg and the colour of the sky respectively. Is the statement made by the student correct or incorrect? Justify.
$(b)$ Which of the two positions correspond closely to the colour of $(i)$ a solution of potassium permanganate,$(ii)$ danger or stop signal lights?