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- Q1 The travel time (T) from district A to district B in a city may be 0.5, 1.0, 1.5, 2.0, 2.5 or 3. and the corresponding probability mass function is given as shown in the figure below. a) Find the mean value of the travel time. b) Find the modal value. c) Find the variance, standard deviation and coefficient of variation of the travel time. d) What is the probability that the travel time will be less than or equal to 1.5 hour P(T <1.5) =? 0.35 0.30 0.3 0.25 0.25 0.20 0.2 ' 0.15 0.10 0.10 0.1 0.05 0.05 0.5 1 1.5 2 2.5 3 I (hours) (1)'dSuppose X is a normal random variable with μ = 40 and σ = 20. Find P(X > 20.2). A) 0.1611 B) 0.8159 C) 0.8389 D) 0.1841 E) 0.8413please slove only part B
- 9. Find the probability of z occurring in the indicated region. J 0 1.751. (See Handout 1, Example 1). The life expectancy of a particular brand of lightbulb is normally distributed with a mean of 1500 hours and a standard deviation of 75 hours. We want to calculate the probability that a lightbulb will last more than 1440 hours. a) Calculate the critical z-score. b) Label the axis and shade the area under the curve that we are interested in. Hours z-score c) What is the probability that a lightbulb will last more than 1440 hours? d) What is the probability that a lightbulb will last less than 1440 hours?4.2 9
- 5. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.5.2-4c. Suppose that the forces acting on columns that help support a building are normally distributed with mean 17.0 kips and standard deviation 2.25. i) Let X be a random variable representing the forces acting on the columns, calculate the probabilities: a) P(X s 20) b) P(15 < X < 20) ii) What minimum force is required to be in the top 4% of columns supporting the building?