RI S2B Binomial Distributions_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _____________________________________________________ Additional Practice Questions for Chapter S2B: Binomial Distribution Page 1 of 5 Additional Practice Questions for Chapter S2B: Binomial Distribution 1 Published articles in medical journals indicate that, on average, 35 out of 100 patients having a lumbar puncture will suffer SSH (‘Severe Spinal Headache’). Twelve patients are given a lumbar puncture. (i) Using a binomial model, find the expected number of patients who will suffer SSH, and find also the standard deviation. [3] (ii) Find the probability that four or more of the twelve patients will suffer SSH. [2] 2 The random variable X ~ B (16, p), where p < 0.5. If the variance of X is 3.36, find the value of p. Find also the probability that X is less than its mean. [4] 3 A factory produces chocolate wh ich are packed into boxes of 20 and delivered to shops for sale. A chocolate will not meet the minimum criteria for packing for sale if it weighs less than 20 grams. On average, 2% of the chocolate produced did not meet the minimum criteria. (i) Find the probability that a randomly chosen box contain at least 1 chocolate that does not meet the minimum criteria. [2] (ii) Find the probability that out of 4 randomly chosen boxes of chocolate, there are exactly 2 boxes with at least 1 chocolate that does not meet the minimum criteria. [2] 4 In a multi-national company with a large population, 13.5% of the staff owns a vehicle. (i) Find the probability that in a random sample of 30 staff, exactly 5 of them will own a vehicle. [2] (ii) The probability that there is at least one st aff who owns a vehicle in a random sample of size n is greater than 0.95. Find the least value of n. [3] 5 Market research showed that 3 out of 10 households in a housing estate subscribe to fibre broadband internet services. (a) 20 households from a particular block of flats in the estate were surveyed. (i) Show that the probability of more than 3 and less than 9 of the households surveyed subscribe to fibre broadband internet services is 0.780, correct to 3 decimal places. [2] (ii) Find the least value of k such that the probability that at most k of the households surveyed subscribe to fibre broadband internet services is at least 0.75. [2] (b) There are a total of 50 blocks of flats in the estate. 20 households from each block of flats were surveyed. Find the probability that there are exactly 39 blocks of flats with more than 3 and less than 9 households surveyed that subscribe to fibre broadband services. [2]

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ _____________________________________________________ Additional Practice Questions for Chapter S2B: Binomial Distribution Page 2 of 5 6 It is known th