Normal Distribution and Engineering Statistics Semester Essay Example
Instructions
- This is a GROUP assignment.
- Each student must be part of a group of 4 or 5 students selected by the lecturer.
- Solutions from each group must be submitted by 19 April 2013.
Special Distributions
Concept of probability (3%)
- Explain why the distribution B(n,p) can be approximated by a Poisson distribution with parameter λ if n tends to infinity, p is greater than 0, and λ = np can be considered constant.
- Show that - and + are the turning points in the graph of the probability density function (p. d. f.) of the normal distribution with mean μ and standard deviation σ.
- What is the relationship between the exponential distribution and Poisson distribution?
Computation of probability (7%)
Let the random v
...ariable X follow a Binomial distribution with parameters n and p. We write X ~ B(n,p).
- Write down all basic assumptions of the Binomial distribution.
- Knowing the probability mass function (p. m. f.) of X, show that the mean and variance of X are E(X) = np and Var(X) = np(1 - p), respectively.
A batch contains 40 bacteria cells, and out of them, 12 are not capable of cellular replication.
What is the probability that, if 3 bacteria cells are randomly chosen without replacement, at least one of them cannot replicate? Now, let's redo problem No. 2, but this time the 3 bacteria cells are chosen randomly with replacement. The number of customers entering a bank in an hour follows a Poisson distribution. To determine the mean and variance of the number of customers in an hour, we need to consider that P(X = 0) = 0.05.
The log-on process in a
large corporate computer network can be represented as a Poisson process with an average rate of 25 log-ons per hour. We need to calculate the probability of no log-ons occurring in a 6-minute interval.
- We also need to determine the probability that a laptop battery lasts more than 6 hours. The time until recharge for a battery follows a normal distribution with a mean of 260 minutes and a standard deviation of 50 minutes.
- Additionally, we must find the first and third quartiles of battery life.
Furthermore, let's assume that the electric power supplied by TNB at any given time follows a normal distribution with a mean of 220 V and a standard deviation of 1 V. Suppose your TV set has the specification of operating within an electric power range of 218 V to 223 V.
What is the likelihood that your TV set is malfunctioning at any given moment?
