RI S3 Normal Distribution_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 ______________________________________________________ Additional Practice Questions for Chapter S3: Normal Distribution Page 1 of 5 Additional Practice Questions for Chapter S3: Normal Distribution 1 A manufacturer produces packets of margarine. The mass of margarine in a packet has a normal distribution with mean 502g and standard deviation 0.8g. Find the proportion of packets which contain less than 500g of margarine. [2] The manufacturer increases the mean am ount of margarine in a packet to  g. The standard deviation remains unchanged. Only 1 packet in 1000, on average, now contains less than 500g. Find  , correct to 1 decimal place. [3] 2 The length of time which an ordinary light-bulb will last may be taken to have a normal distribution with mean 600 hours and standard deviation 100 hours. The length of time for which a new ‘long life’ bulb will last may be taken to have a normal distribution with mean 2000 hours and standard deviation 200 hours. (i) One ordinary bulb is chosen at random. Fi nd the probability that it will last for more than 450 hours. [2] (ii) Two ordinary bulbs are chosen at random . Find the probability that the sum of the times for which they last will be less than 1100 hours. [3] (iii) One ordinary bulb and one long-life bu lb are chosen at random. Find the probability that the long-life bulb lasts for more than three times as long as the ordinary bulb. [3] The total time in which 10 ‘long life’ bulbs will last is denoted by W hours. Find the value of t (to the nearest hour) such that P( ) 0.75Wt . [3] 3 [The notation 2N( , ) denotes a normal distribution with mean  and variance 2 .] The school bus leaves the stop near Ben’s home at X minutes past 8.00 a.m., where X is an 2N(20,3 ) random variable. Ben reaches the bus stop at Y minutes after 8.00 a.m., where Y is an 2N(15,2 ) random variable, X and Y being independent. Find the probability (to three decimal places) that Ben misses the bus. [2] The ride from this stop to the school lasts T minutes, where T is an 2(30,( 7) )N random variable, independent of X. The random variable W is the number of minutes before 9.00 a.m. at which the bus arrives at the school. Express W in terms of X and T. [1] Calculate the mean and variance of W and find, to three significant figures, the probability that the bus arrives at the school after 9.00 a.m. [2]

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ ______________________________________________________ Additional Practice Questions for Chapter S3: Normal Distribution Page 2 of 5 4 Chickens and turkeys are sold by weight. Th e masses, in kg, of chickens and turkeys are modeled as having independent normal distributions with means and standard deviations as shown in the table.