NYJC Normal Distribution Tutorial Q4

In this question, you should state clearly all the distributions that you use, together with the values of the appropriate parameters.

A workshop employs craftspeople to make wooden souvenirs for sale at a tourist attraction. Typically, the time taken to make a wooden souvenir by a skilled craftsperson follows a normal distribution with a mean of \(1.2\) hours and a standard deviation of \(10\) minutes. A workday at the workshop is \(8\) hours long (with a lunch break given separately). It may be assumed that a skilled craftsperson will start making the next souvenir once the previous one is completed.

1. Find the probability that a skilled craftsperson is able to make \(7\) wooden souvenirs in a workday.[2]
2. Two skilled craftspeople start work at the same time. Find the probability that they make their first wooden souvenir of the workday within \(15\) minutes of each other.[3]
3. Find the probability that a skilled craftsperson is unable to make the \(7\)th souvenir in a workday. Hence find the probability that a skilled craftsperson makes exactly \(6\) wooden souvenirs in a workday.[3]
4. The time taken by an apprentice of a particular skilled craftsperson to make a wooden souvenir is \(1.5\) times the time taken by the skilled craftsperson. Find the probability that the total time taken to make \(3\) wooden souvenirs by the apprentice is longer than \(4\) times the time taken by the skilled craftsperson to make a wooden souvenir. State the assumption needed for your working.[4]