Problem 1: The 68%-95%-99.7% rule tells us that for data that follows a normal distribution, the probability that a measurement falls within one standard deviation from the mean is 68%, the probability that a measurement falls within two standard deviations from the mean is 95%, and the probability that a measurement falls within three standard deviations from the mean is 99.7%. How can we express the interquartile range of a normal distribution in terms of standard deviation?

Problem 2: A random variable has a normal distribution with ?? = 62.4. Find the standard deviation of the random variable if the probability is 0.20 that it will take on a value greater than 79.2

Problem 3: The 12 observations below represent peak particulate matter measurements from various sites across the US in units of ??g/m³.

30, 45, 22, 51, 24, 48, 28, 33, 79, 24, 45, 31.

Could a normal probability model be used to anticipate peak particulate values in the future? If not, how might you find a more suitable distribution to use? Use the probability paper posted on blackboard to answer this question, and verify your answer using Minitab.