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Referring to the box plots , the sides of the "box" are at the first and third quartiles, and the difference between these (the length of the box) is called the interquartile range (IQR). A mild outlier is an observation that is between 1.5 and 3 IQRs from the box, and an extreme outlier is an observation that is more than 3 IQRs from the box.
a. If the data are normally distributed, what percentage of values will be mild outliers? What percentage will be extreme outliers? Why don't the answers depend on the mean and/or standard deviation of the distribution?
b. Check your answers in part a with simulation. Simulate a large number of normal random numbers (you can choose any mean and standard deviation), and count the number of mild and extreme outliers with appropriate formulas. Do these match, at least approximately, your answers to part a?
Use RNG in Excel to generate n = 5 observations from the Normal distribution N(20, 5). Test H0: μ = 20 versus H0: μ ≠ 20 at the α = 0.05 level of significance. Repeat this process 100 times and then count the number of times that you reject H0.
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the lenght of time x to complete a standard achievement test is approximately normally distributed with a mean of 58
Kyle averages 7 finished accounts a day. His standard deviation is 2 account per day and we wish the probability that Kyle will finish day with more than 8 finished accounts. Probability will be?
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