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Example I measures at least ±1 gram wrong? A weight has a measurement error, E, that can be described by a standard normal disrtribution, i.e. E ∼ N (0, 12) that is, mean µ = 0 and standard deviation σ = 1 gram. We now measure the weight of a single piece a) What is the probability that the weight measures at least 2 grams too little? b) What is the probability that the weight measures at least 2 grams too much? c) What is the probability that the weight 1 2 Example II Example III It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal distribution with mean µ = 280.000 and standard deviation σ = 10.000. It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal distribution with mean µ = 290.000 and standard deviation σ = 4.000. a) What is the probability that a randomly selected teacher earns mor than 300.000? a) What is the probability that a randomly selected teacher earns mor than 300.000? 3 4 Example IV Example V It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal distribution with mean µ = 290.000 and standard deviation σ = 4.000. In a dose-response experiment with 80 rats, it is assumed that the probability that a rat survives the experiment is p = 0.5. a) Give the salary interval that covers 95% of all teachers salary a) What is the probability that at most 30 rats die in the experiment? b) What is the probability that between 38 and 42 rats die in the experiment? 5 6 Example VI Example VII The particle size (µm) in a compoundi is assumed to follow a Log-normal distribution with α = 0.73 and β = 0.44. The particle size (µm) in a compoundi is assumed to follow a Log-normal distribution. We have the oberservations: 2.2 3.4 1.6 0.8 2.7 3.3 1.6 2.8 1.9 What is the proportion of particles with a size in the interval [2; 3] We take the logarithm of the data and achieve: 0.8 1.2 0.5 -0.2 1.0 1.2 0.5 1.0 0.6 from which we get: x̄ = 0.733 and s = 0.44. What is the proportion of particles with a size in the interval [2; 3] 7 8 Example VIII Students in a course arrive to a lecture between 7.45 and 8.15. It is assumed that the arival times can be described by a uniform distribution. What is the probability that a randomly selected student arrives between 8.05 and 8.15? What is the probability that a randomly selected student arrives after 8.15? 9