Question 2 [Total = 20 marks]

A total of 12 players consisting 6 male and 6 female badminton players are attending a training camp.

(a)During a morning activity of the camp, these 12 players have to randomly group into six pairs of two players each.

(i)Find the total number of possible ways that these six pairs can be formed. (4 marks)

(ii)Find the probability that each pair contains players of the same gender only.Correct your final answer to4 decimal places. (6 marks)

(b)During an afternoon activity of the camp, 6 players are randomly selected and 6 one-on-one

matches with the coach are to be scheduled.

(i)How many different schedules are possible? (2 marks)

(ii)Find the probability that the number of selected male players is higher than that of female players given that at most 4 females were selected.Correct your final answer to 4 decimal places.

Question 3 [Total = 15 marks]

Suppose the weight of a pack of sugar manufactured by a certain company is normally distributed with an average of 50 grams and a standard deviation of 9 grams.

(a)What is the probability that a randomly selected pack of sugar is weighted 40grams to 56grams?Correct your final answer to4 decimal places.(4 marks)

(b)The management would like to screen out those packs of sugar with weight belowKgrams. Find the value ofKsuch that 5% of the packs of sugar would be screened out.Correct your final answer to1 decimal place. (4 marks)

(c)Suppose a random sample of 400 packs of sugar is selected. Find the probability that at least 119 packs have weights more than 54 grams each by using continuity correction method.Correct your final answer to4 decimal places. (7 marks)