In a population, 95% of adults weigh between 50-80kg. Assuming a standard normal distribution, show your calculations and show on a standard normal distribution diagram: (5 marks) (a) The mean (b)The adult weights that correspond to the following z-scores: -3.5, -2.5, -1, +0.5, 2, 3. 6. A manufacturing company produces tires at a cost of $75 each. The following are probabilities of defective tires in a given production run: probability of no defective tires 8%; probability of 1% defective tires 30%; probability of 2% defective tires 37%; probability of 3% defective tires 25%. When a defective tire is detected, it must be removed from the assembly line. The tire is discarded, and replaced by another tire, both at the full $75 cost. This process also adds an extra $6 to the cost to install the replacement tire. a) What is the expected total cost to the company of a batch of 4,000 tires? Show your calculations. (10 marks)

Explain it clearly and need only typed answers Thank you