RI S4 Sampling_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 ______________________________________________ Additional Practice Questions for Chapter S4: Sampling Page 1 of 5 Additional Practice Questions for Chapter S4: Sampling 1 A manufacturer of candles claimed that it produced birthday candles with a mean burning time of 6 minutes. A random sample of 150 birthday candles was tested and the burning times, X minutes, were summarized by 120)5(  x and 2( 5) 638.x  Calculate the unbiased estimates for the mean  and variance 2. [3] 2 Two firms A and B manufacture similar components with mean breaking strengths of 6 units and 5.5 units, and standard deviations 0.4 units and 0.25 units respectively. It is given that both distributions are normal. If random samples of 100 components from firm A and 50 from firm B are tested, find the probability that the mean breaking strength of the sample from firm A minus that from firm B will be between 0.45 and 0.55 units. [3] 3 The life, in hours, of a randomly chosen light bulb produced by a manufacturer is normally distributed with mean 1100 and standard deviation 70. How large a sample is required such that the probability that the mean life in the sample shall exceed 1120 is not more than 5%? [5] Do you need to use Central Limit Theorem in your working? Explain. [1] 4 The times taken by two runners A and B in a 400 metre race are independent and may be assumed to be normally distributed. The times (in seconds) taken by A has mean 46 and standard deviation 0.5 and the times taken by B has mean 46.2 and standard deviation 0.8. LetX denote the average time for A to run the 400 metre track on 10 different occasions and Y denotes the average time for B to run the same track on 16 different occasions. Find the value of t such that  P 0.2 0.1X Y t    . [4]

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ ______________________________________________ Additional Practice Questions for Chapter S4: Sampling Page 2 of 5 5 In a certain examination with a very large entry, the marks obtained by the male candidates were found to follow a normal distribution with a mean of 54 and a standard deviation of 16.X denotes the mean mark scored by a sample of 4 male candidates. (i) State the sampling distribution of X. (ii) Find the probability that X will exceed 70. (iii) Given that there is a probability of 0.95 that X differs from its mean mark by less than c, find the value of c. In the same examination the marks obtained by the female candidates were found to follow an independent normal distribution with a mean of 59 and a standard deviation of 20. (iv) Find the probability that the total marks obtained by a randomly chosen male candidate and a randomly chosen female candidate excee