SAJC Check your Understanding Binomial dist_solutions

Binomial Distribution: Check your Understanding Section 1: Assumptions 1. ACJC Prelim 8865/2018/Q7part A candy factory manufactured a large amount of pastilles daily and their candies are randomly packed in boxes of 20. The probability of selecting an orange-flavoured pastille to be packed into a box is 0.25. The random variable X is the number of orange-flavoured pastilles in a box of 20 pastilles. State an assumptions that is needed for X to be modelled by a binomial distribution. [2] Soln: A pastille being orange-flavour is independent of any other pastille being orange flavor. Or The flavour of each pastille must be independent of the flavour of any other pastille. 2. AJC Prelim 8865/2018/Q7part On average 7% of a certain brand of kitchen lights are faulty. The lights are sold in boxes of 12. State, in context, two assumptions needed for the number of faulty lights in a box to be well modelled by a binomial distribution. [2] Soln: A kitchen light being faulty is independent of any other kitchen light being faulty. The probability of a light being faulty is constant at 0.07 for every lights in a box. 3. CJC Prelim 8865/2018/Q6part As part of Singapore’s aim to be a Smart Nation in 10 years, hawker centres are encouraged to go cashless. An initial trial of cashless payment in hawker centres shows that 1 in 5 customers uses cashless payment. A random sample of 12 customers is selected and the number of customers who use cashless payment is denoted by the random variable C. State, in context, an assumption needed for C to be well modelled by a binomial distribution. [1] Soln: A customer who uses cashless payment is independent of any other customers who use cashless payment. The probability of customers using cashless payment is constant at 0.2 for every customers. Section 2: Find Probability 1. YJC Promo 8865/2018/Q6 A health agency launches a ‘2+2’ campaign to encourage people to eat two servings of fruits and two servings of vegetables per day. In a particular school, 20% of students eat at least 2+2 fruits and vegetables per day. 18 students in the school are selected at random and the number of students who eat at least 2+2 fruits and vegetables per day is denoted by X. (i) Find the probability that more than 3 of them eat at least ‘2+2’ fruits and vegetables per day, [2]

(ii) Find the probability that between 2 and 7 of them eat at least ‘2+2’ fruits and vegetables per day, [2] Answer: (i) 0.499, (ii) 0.677 Soln: (i)  ~ B 18,0.2X ( 3) 1 ( 3) = 0.499 P X P X    (ii)      P 2 7 P 6 P 2 0.9481290011 0.271348775 0.677 (3 s.f.) X X X        2. RI Prelim 8865/2018/Q8part A dental clinic sees 50 patients each day for a total of 6 days each week, and is closed on Sunday. On average, 30 % of the patients are eligible for a dental subsidy after treatment, and the eligibility of a patient for dental subsidy is in