# Normal Distribution and Engineering Statistics Semester

SSCE 2193 Engineering Statistics Semester 2, Session 2012/2013 ASSIGNMENT (10%) Instructions: a. This is a GROUP assignment. b. Each student must be a member of a group of 4 or 5 students, selected by lecturer. c. Solutions from each group must be submitted by 19 April 2013. SPECIAL DISTRIBUTIONS I. Concept of probability (3%) 1. Explain why the distribution B(n,p) can be approximated by Poisson distribution with parameter if n tends to infinity, p 0, and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p. d. f. f normal distribution with mean and standard deviation . 3. What is the relationship between exponential distribution and Poisson distribution? II. Computation of probability (7%) 1. Let the random variable X follow a Binomial distribution with parameters n and p. We write X ~ B(n,p). * Write down all basic assumptions of Binomial distribution. * Knowing the p. m. f. of X, show that the mean and variance of X are = np, and 2 = np(1 – p), respectively. 2. A batch contains 40 bacteria cells and 12 of them are not capable of cellular replication. Suppose you examine 3 bacteria cells selected at andom without replacement. What is the probability that at least one of the selected cells cannot replicate? 3. Redo problem No. 2 if the 3 bacteria cells are selected at random with replacement. 4. The number of customers who enter a bank in an hour follows a Poisson distribution. If P(X = 0) = 0. 05, determine the mean and variance of the number of customers in an hour. 5. In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of 6 minutes? 6.

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. * What is the probability that a battery lasts more than 6 hours? * What are the first and third quartiles of battery life? 7. Suppose that electric power supplied by TNB at any time follows normal distribution with mean 220 V and standard deviation 1 V. Let your TV set have the specification of electric power between 218 V and 223 V. What is the probability that at a certain time, your TV set is not functioning properly?

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