Q1, A Small Medium Enterprise (SME) is concerned about the time taken by their production staff in completing a repetitive task in the production line. The production manager found that the length of time taken to complete production line task is normally distributed. The mean length of time to complete task was found to be 3.0 minutes and with a standard deviation of 0.40 minutes.

i)What is the probability that the time taken to complete the task being more than 3.5 minutes? [0.5 mark]

ii)What is the probability that the time taken to complete the task will be between 2 minutes and 3.5 minutes? [1.5 marks]

iii)Find the length of time (in minutes) required to complete the task in the production line for the lower 5% of the time taken to complete the task.

iv)A random sample of 5 production task was taken from the production line. Find the probability that the sample mean is more than 3.5 minutes to complete a repetitive task in the production line. [2 mark