1 (Binomial) Students 2023 (SAJC)

1 ST ANDREW’S JUNIOR COLLEGE JC2 H1 MATHEMATICS (8865) Term 3 Weekend Assignment 1 Topic: Binomial Distribution Name: ______________________________ Marks:________/11 C.G.: __________ 1. TJC Promo 8865/2021/Q9 CheapnGood is an online shop that s ells solar powered lights. CheapnGood is not very reliable and it is known that p% of their solar powered lights do not work. A shopper bought 12 solar powered lights for his garden from CheapnGood. The 12 lights were randomly chosen by CheapnGood and delivered to the shopper. For part (i) to part (iv), take p = 15. (i) Find the probability that exactly 7 lights bought by the shopper work. [1] (ii) Find the probability that at least 3 lights bought by the shopper do not work. [2] (iii) Find the probability that exactly 7 lights work given that at least 3 lights bought by the shopper do not work. [3] (iv) Find the least value of r such t hat the probability th at less than r lights bought by the shopper do not work is greater than 0.9. [3] In a random sample of size 12, find in terms of p, the mean and variance of the number of lights that do not work. [2]