For this exercise, you can use the table of the cdf of the standard normal distribution in Figure 1. The measurement of atmospheric ozone concentration (in µg/m³) is modeled by a random variable X with distribution N(m, o2) with o² = 3.1. 1. Write the statistical model. 2. In many applications, data are often modeled with the Normal distribution, while often the observed values are by definition positive (e.g. weight, size, speed, duration). Can you explain why? 3. Some day, we make some measurements and we assume that this day the ozone concentration is178µg/m³ (yet the experimenter doesn't know this concentration otherwise he wouldn't need measure-ments). (a) Compute the probability that a unique measurement is greater than 180? (b) What is the probability that the mean of three measurements is greater than 180 ? (c) How many measurements are necessary for the probability that the mean of these measurements is greater than 180 being less than 1%?

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