MDM4U Names Dotes THINKING 7. Using calculus, it can be shown that the area under the exponential distribution curve is P(X x)=1-e The manager of the local bank knows that the average length of time it takes to serve one client is 3.5 min, How likely is it that the next customer served will have to wait longer than 5 minutes? [3 marks] 8. Flooring materials being produced at a lumber mill have an average thickness of 7.9 mm, with a standard deviation of 0.4 mm. a) What range do about 68% of the flooring materials fall within? [2 marks] b) If you wanted 95 % of the materials to fall within the range 7.5 mm and 8.3 mm, what mean and standard deviation would be required? [3 marks] 9. A car assembly line produces 1920 cars per shift. A defective rate of 3% is considered acceptable. From the production of one recent shift, 60 cars were found to be defective. Find the probability of this occurrence and explain to the shift supervisor what your answer means and whether changes will need to be made in the production process to reduce the number of defective cars, [6 marks] Page 3 of 4