Question 1:
Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the door can be opened; a yellow light indicates that the door is locked from the inside. Suppose that 90% of the time when the card is inserted, the door should open and a green light will appear with probability 0.98. When the door should not open a green light may still appear (electronic error) 5% of the time. Suppose a card has just been inserted and the light is green.
What is the probability that the door will actually open. Supply a probability tree with your solution.
A retail company predicted that its turnover for next year will be $4500000 and that the costs will be $4000000. However, there are a number of factors that affect both the turnover and costs. Assuming that both turnover and costs have normal distributions, each with a standard deviation of $250000, what is the probability that the company makes a profit?
An industrial chemical is packaged and sold in 20-kg plastic bags. To minimize the number of underweight sacks, the filling process has been adjusted so that the mean is 21 kg. The weight of the sacks varies because of the nature of the product. Assume that the weight has a normal distribution with a standard deviation of 2.5 kg.
Determine the probability of an underweight sack.
If the sacks can be bought in batch quantities of 30, calculate the probability that the average weight per sack in a batch, is less than 20 kg.