A quality control officer is checking on the assembly times for different types of electronic compon

Question

A quality control officer is checking on the assembly times for different types of electronic components in a factory. The assembly times, in minutes, for microchips and circuit boards follow independent normal distributions with given means and standard deviations as shown in the table. MeanStandard deviation Microchips$45$$7$ Circuit Boards$75$$10$ It is known that $85$% of circuit boards take no more than $t$ minutes to assemble. Find the value of $t$.[2] Find the probability that the assembly time for a randomly chosen microchip takes more than $50$ minutes.[1] Microchips are randomly chosen for inspection. Find the probability that the assembly time of the $10^{\mathrm{th}}$ microchip is the $2^{\mathrm{nd}}$ microchip that takes more than $50$ minutes to assemble.[3] On a particular day, the factory needs to assemble $6$ microchips and $4$ circuit boards. Find the probability that the total assembly time for these randomly chosen components is less than $500$ minutes.[3] The factory charges $\ 0.70$ per minute for the assembly of a circuit board. Find the probability that the total revenue from assembling $6$ randomly chosen microchips and $4$ randomly chosen circuit boards exceeds \$$\ 350$.[4]

Accepted Answer

(i)t=85.4 (ii)0.238 (iii)0.0580 (iv)0.00394 (v)0.380

2024 TMJC H1 Q12

2024 TMJC H1 Q12