A hint to get started
Match height questions to the correct probability model
In a nation, men’s heights are normal with mean 1.70 m and standard deviation 10 cm; women’s heights are normal with mean 1.60 m and standard deviation 7.5 cm.
(i) Three men are selected at random: find the probability that one is taller than 1.83 m, one is shorter than 1.7 m and the other is between 1.7 m and 1.83 m.
(ii) Five men are selected at random: find the probability that exactly 3 are taller than 1.83 m.
(iii) Find the probability that the average height of 3 men and 2 women chosen randomly exceeds 1.68 m.
(iv) Find the probability that a husband and wife have not more than 5 cm difference in heights.
(v) State the assumptions made for (iii) and (iv).
CJC · Lecture · Example 10
The Teacher supplies the ordering result in(i), binomial model/result in(ii), complete sum and absolute-difference working in(iii)/(iv), and highlights the assumptions issue with an examiners’ report pointer.
Exactly three tall men is a binomial count. One in each of three different categories is an ordering calculation. Neither is found by adding three normal heights.