A manufacturing plant processes raw material for a supplier. An order placed with the plant is consi

Question

A manufacturing plant processes raw material for a supplier. An order placed with the plant is considered to be a bulk order when a worker is expected to process more than $300$ kg (kilograms) of raw material. Albert uses a machine to process $X$ kg of raw material and Bob uses a separate machine to process $Y$ kg of raw material on a working day. $X$ and $Y$ are independent random variables with the distributions $\mathrm{N}\left( 296,{{8}^{2}} \right)$ and $\mathrm{N}\left( 290,{{12}^{2}} \right)$ respectively. Find the probability that Albert processes more than $300$ kg of raw material on a randomly selected working day.[2] Find the probability that, over a period of $15$ independent working days, there are exactly four working days on which Albert processes more than $300$ kg of raw material. [2] Find the probability that the total amount of raw material Bob processes over two working days exceeds twice the amount of raw material Albert processes on one working day. [4] The plant receives a bulk order and Albert wants to have a probability of at least $0.95$ of meeting the order. This can be done by changing the value of $\mu $, the mean amount of raw material Albert processes using the machine, but the standard deviation remains unchanged. Find the least value of $\mu $.[3]

Accepted Answer

(i) $0.309$ (ii) $0.214$ (iii) $0.303$ (iv) $314$

2017 TPJC P2 Q8

2017 TPJC P2 Q8