In this question, you should state clearly all the distributions that you use, together with the val

Question

In this question, you should state clearly all the distributions that you use, together with the values of the appropriate parameters. A company produces two types of yarn balls with two machines. Machine A produces balls of 2-ply yarn. Over a period of time, it is found that 80% of the balls of yarn from Machine A have lengths less than 340 metres and 10% of the balls of yarn from Machine A have lengths less than 280 metres. Assuming that the lengths, in metres, of yarn in balls of 2-ply yarn from Machine A follows the distribution $N(\mu, \sigma^2)$, find $\mu$ and show that $\sigma = 28.3$.[3] For the rest of the question let $\mu = 300$ and $\sigma = 20$. Machine B produces balls of 3-ply yarn. The lengths, in metres, of yarn in balls of 3-ply yarn from Machine B follows the distribution $N(220, 6^2)$. Five balls of 3-ply yarn from Machine B are randomly chosen. Find the probability that two of them have lengths more than 230 m and three of them have lengths less than 215 m.[2] The probability that two randomly chosen balls of 2-ply yarn from Machine A and three randomly chosen balls of 3-ply yarn from Machine B have total length exceeding $k$ metres is 0.385. Find the value of $k$, correct to 2 decimal places.[3] A technician changed the settings on the two machines. The lengths of yarn in balls of 2-ply yarn from Machine A is reduced by 9% and the lengths of yarn in balls of 3-ply yarn from Machine B is reduced by 5%. Find the probability that the total length of yarn in three randomly chosen balls of 2-ply yarn from Machine A is within 50 metres of the total length of yarn in four randomly chosen balls of 3-ply yarn from Machine B.[4]

Accepted Answer

(a)28.3 (b)0.000189 (c)1268.81 (d)0.815

2025 JPJC P2 Q10

2025 JPJC P2 Q10