Assignment 4 Material from Module 6 Questions Total of marks is 31. Question 1 – 12 marks (a) The mean weight for a bird in a population is 31g. and the standard deviation is 0.2g. The distribution of weights is normal. Determine (i) the probability that the weight for a randomly selected bird exceeds 30.5g, [2 marks] (ii) the probability that the weight for a randomly selected bird is between 30.5g and 31.5g. [2 marks] (iii) A bird is classied as underweight if its weight is less than 30.4g. What is the probability that at least 1 bird in a sample is underweight. [4 marks] Data Source: Statistics and data with R. Y. Cohen & J. Cohen, Wiley (2008). (b) The voltage in an electric circuit has a normal distribution with mean 120 and stan- dard deviation 2. If 3 independent measurements of the voltage are made, what is the probability that all 3 measurements will be between 116 and 118? [4 marks] Data Source: Probability and Statistics M. DeGroot & M. Schervish, Addison-Wesley (2002). Question 2 – 8 marks A system contains 3 components that function independently of each other and are connected in series. The system fails as soon as one of the components fails. The lifetime of the rst component, measured in hours, has an exponential distribution with rate ?? 1 = 0:001; the second is exponentially distributed with rate parameter 2 = 0:003 and the third has an exponential distribution with rate 3 = 0:006. Determine the probability that the system will not fail before 100 hours. Data Source: Probability and Statistics M. DeGroot & M. Schervish, Addison-Wesley (2002). Question 3 – 4 marks A random variable X > 0 has a probability density function f and a distribution F. A hazard function is dened h(x) = f(x) 1 ?? F(x) x > 0 show that if X has an exponential distribution, the hazard function h(x) is constant. Data Source: Probability and Statistics M. DeGroot & M. Schervish, Addison-Wesley (2002). 1
Question 4 – 7 marks Response times on a computer terminal have an…