15% 1 hour ANSWER ALL QUESTIONS 1. a) An experiment is conducted to select a suitable catalyst for the production of a dispersant for cleaning oil spill in Straits of Malacca.
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Suppose Ir. Aziz, the chemical engineer randomly selected three catalysts for testing from 10 different proposed catalysts. Four of the catalysts have high acidity level and six of the catalysts have low acidity level.
Calculate the probability that not more than one high acidity level catalyst is selected. [4 marks] b) Potholes on a highway can be a serious problem and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that, on the average, 2 potholes per kilometre after a certain amount of usage.
It is assumed that the Poisson process applies to the random variable for the number of potholes. i. What is the probability that there will be between 3 and 9 potholes in a given section of 5 km. 2 marks] ii. the What is the probability that there will be more than 3 km section before next pothole is found.
[3 marks] 2. A corporation buys motors for electric fans from company M that guarantees 95% of its motors are nondefective and it will replace all defective motors at no cost. The motors are received in large shipments. Assume that motor selections are independent events. i. What is the probability that the eighth motor selected from a shipment is the third motor found to be defective? [3 marks] ii.
The quality control department at the corporation randomly selects 20 motors from each shipment and inspects them for being good or defective. If the sample contains more than two defective motors, the entire shipment is rejected. What is the probability that a given shipment of motors received by the corporation will be rejected. [3 marks] 3. a) The length of stay for foreign engineering students in Malaysian higher learning institutions may due to several factors such as type of registration, study completion time and financial support.
A study is conducted in a local university college shows that the length of stay of a foreign engineering student from country A is approximately normally distributed with mean 1050 days and standard deviation of 25 days. A foreign engineering student from country A is selected at random, what is the probability that her/his stay exceeds three years? Assume 1 year = 365 days. [3 marks] b) Lifetime of a head projector light bulb follows normal distribution with mean ? 28 hours and standard deviation ? hours. i. A random sample of size n = 25 is drawn from the population of light bulbs.
If ? = 0. 5 hours, what is the probability that the sample mean, X will exceed ? + (0. 5) ? ? [2 marks] ii. A random sample of size n is to be drawn from that population. ?? Determine the value of n if, after that sample has been drawn, we want the difference between the sample mean, X and the population mean, ? is less than (0. 25)? with probability 0.
95[ P(| X – ? |