(Solved): Answer any 2 of the following questions i.e. Q5(a), Q5(b) or Q5(c). There are ...

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Answer any 2 of the following questions i.e. Q5(a), Q5(b) or Q5(c). There are equal marks for both questions. For each answered question explain your answers i.e. show your reasoning. Q 5(a) [12.5 Marks] In a certain population, woman have heights which are normally distributed with a mean of \( 165 \mathrm{~cm} \) and a standard deviation of \( 7 \mathrm{~cm} \). Men have heights which are normally distributed with a mean of \( 179 \mathrm{~cm} \) and a standard deviation of \( 7 \mathrm{~cm} \). You can assume there are an equal number of men and women in the population. (i) Above which height is a person more likely to be male? (ii) If the standard deviation for the height of men was \( 3 \mathrm{~cm} \) instead of \( 7 \mathrm{~cm} \), how this would change your answer to the previous question? Explain.