1. [13 marks] Suppose you are a member of a team of quality assurance specialists. Your team wants to determine whether a product meets engineering design specifications provided by the product design team. Your team gathers a sample of 36 units of product, and you measure the height of each unit, in millimetres. a) [5 marks] Suppose the population standard deviation is 0.65 mm, and the engineering design specifications state that the population mean height must be 90 mm. What is the probability of obtaining a sample mean height less than 89.8 mm, if the population mean height is 90 mm? Declare the random variable of interest, show the probability you are asked to calculate, how you standardize, your z-score (rounded to 2 decimal places if rounding is necessary), and your final answer (rounded to 4 decimal places if rounding is necessary).