1 The service time at an automobile center has a Lognormal distribution with parameters =1.0 and mean of 3.4. (a) (b) (c) (d) (e) What is the probability that a customer will have to wait for more than 4.69 hours? What is the probability that at least 8 of the next 10 customers will have to wait for more than 4.69 hours? What is the expected number of customers that will have to wait more than 4.69 hours? What is the median service time? What is the 95th percentile of service time? Problem 2 A service station will be supplied with gasoline once a week. Its weekly volume of sales, T, in 10,000 of gallons, is described by the probability density function f ( t )=t e t 2 2 for t >0 Determine the capacity if its underground tank so that the probability that its supply will be exhausted in a given week is to be 0.01. What is the expected sales volume? Problem 3 The demand for the number of spares, X, to support a squadron of F/A-27 aircraft for a month of deployed operations can be described by a normal distribution with =35 and =8 (a) If the number of spaces, for the deployment is the standard number of 40, what is the probability of not having enough, i.e., the demand exceeds the supply? (b) How many spares are required for the deployment if the probability of having enough is 90%? (c) What is the probability of needing more than 40 spares, given the demand is at least 35? Problem 4 Determine the value of c so that ( )( ) 4 for x=0,1,2,3 p ( x )=c 3 x 3x is a probability mass function. Then find the mean and variance of x. Plot the probability mass function and probability distribution function of x. Problem 5 (a) The random variable X is the number of on-board computer module failures per year in an executive fleet. The probability distribution function of X, F(x), is shown below: Probability Distribution Function F(x) 1.0000 0.9000 0.8000 0.7000 0.6000 F(x) 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0 1 2 3 4 5 6 x What is the probability that the number of on-board computer module failures per year in executive fleet will be: 1) less than 2? 2) between 2 and 4? 3) at least 2? 4) no more than 2? 5) What is the expected number of on-board computer module failures? 6) What is the standard deviation? (b) The random variable T is the time to develop requirements for a new software application. The probability distribution function, F(t), is shown below: Probability Distribution Function F(t) 1 0.9 0.8 0.7 0.6 F(t) 0.5 0.4 0.3 0.2 0.1 0 50 60 70 80 90 100 110 120 130 140 150 t What is the probability that the value of T will be 1) Less than 90? 2) Between 80 and 110? 3) Greater than 110, given that the value of T is greater than 100