1.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:

(a) The mean

(b) The adult weights that correspond to the following z-scores:

-3.5, -2.5, -1, +0.5, 2, 3.

2.A manufacturing company produces tires at a cost of $65 each.The following are probabilities of defective tires in a given production run: probability of no defective tires 8%; probability of 1% defective tires 32%; probability of 2% defective tires 35%; 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.This process adds an extra $6 to the cost to install the replacement tire.

a)What is the expected cost to the company of a batch of 4,000 tires?Show your calculations.

b)What would be the cost to the company to produce the same batch of 4,000 tires if there were no defects?