2. [5 marks] Suppose you are a member of a board of directors of a large company. The product design team has been working on a new product. They present you with a report that indicates the planned population mean weight of the units of product is 85g, with a population standard deviation of 10g. The company completes a test run of the production system: they create 36 units of product. What is the probability that these 36 units have a sample mean weight within 1% of the planned population mean weight? Hint: For example, suppose the planned population mean weight were, say, 1234. By "within 1% of the planned population mean weight", I mean "from 1234 - (1234*0.01) = 1221.66 to 1234+ (1234*0.01)=1236.44". So, I would need to find the probability that I get a sample mean between 1221.66 and 1236.44 when I sample 36 values from the population of all unit weights. a) [1 mark] Declare the random variable of interest: b) [1 mark] Figure out what "within 1% of the planned population mean" means (see the hint above for help with that part - copy/paste and change values!). c) [3 marks] State the probability using proper notation (i.e., P(something)) and calculate it. Show your work. Round your final answer to 4 decimal places, even if there are trailing Os (that means if your final answer is, say, 0.5000, then don't write 0.5 - include all those "extra" Os).