In a large shipment of second-hand T-shirts, $4$% of the T-shirts are torn. The T-shirts are sold

Question

In a large shipment of second-hand T-shirts, $4$% of the T-shirts are torn. The T-shirts are sold in boxes of $25$ pieces each. Let $X$ denote the number of torn T-shirts in a box. State, in the context of the question, two assumptions needed to model $X$ by a binomial distribution.[2] You are now given that $X$ can be modelled by a binomial distribution. A box is randomly chosen. Find the probability that a box contains at least $2$ torn T-shirts.[2] A box is deemed to be of inferior quality if it contains at least $2$ torn T-shirts. Find the probability that, in a random sample of $10$ boxes of T-shirts, more than $3$ boxes are of inferior quality.[2] A distributor purchases a batch of $60$ boxes of T-shirts. Find the probability that the average number of torn T-shirts per box is more than $1.1$.[3] Find the most probable number of boxes of inferior quality in the batch.[2] In a large shipment of second-hand blouses, a proportion $p$ of the blouses is torn. The blouses are also sold in boxes of $25$ pieces each. The number of torn blouses in a box follows a binomial distribution. It is known that the probability of a box containing exactly $2$ torn blouses is $0.206$. Write down an equation satisfied by $p$. Hence, find the value of $p$, given that $p > 0.1$.[2]

Accepted Answer

(b)0.264 (c)0.258 (e)16 (f)$300p^2(1-p)^{23}=0.206$, p=0.130

2025 YIJC P2 Q11

2025 YIJC P2 Q11