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Empirical rule percentages7/24/2023 ![]() ![]() Since 3 / 4 of 50 is 37.5, this means that at least 37.5 observations are in the interval. By Chebyshev’s Theorem, at least 3 / 4 of the data are within this interval. Thus statement (6) must definitely be correct. Because the empirical rule gives you the percentages of the total data (if normally distributed) that are between or above or below values that are one. Solution: The interval (22, 34) is the one that is formed by adding and subtracting two standard deviations from the mean. Statement (4) is definitely correct and statement (4) implies statement (6): even if every measurement that is outside the interval (\(675,775\)) is less than \(675\) (which is conceivable, since symmetry is not known to hold), even so at most \(25\%\) of all observations are less than \(675\).The percentage of the data spanning the 2nd and 3rd SDs is 13.5 2.35 15.85 The probability that a randomly chosen basketball will have a diameter between 9.5 and 10.5 inches is 15.85. But this is not stated perhaps all of the observations outside the interval (\(675,775\)) are less than \(75\). This reading on the Empirical Rule is an extension of the previous reading Understanding the Normal Distribution. This would be correct if the relative frequency histogram of the data were known to be symmetric. As seen in the normal curve, the Empirical Rule (68-95-99.7 Rule), states that approximately: 68 of the data will fall within one standard deviation of the. Given: µ 25 3 Now, using the Empirical rule formula, first standard deviation µ - to µ (25-3) to (25 3) 22 to 28. Solution: To find: percentage chance of 19 to 31 people at the store. The Empirical Rule states that approximately 68 of the IQ scores in the population lie between 90 and 110, approximately 95 of the IQ scores in the population lie between 80 and 120, and approximately 99. Empirical Rule If the data are normally distributed: 68 of the observations fall within 1 standard deviation of the mean. Statement (5) says that half of that \(25\%\) corresponds to days of light traffic. Find the percentage chances of people arriving are 19 to 31 at the store. Statement (4), which is definitely correct, states that at most \(25\%\) of the time either fewer than \(675\) or more than \(775\) vehicles passed through the intersection.Statement (4) says the same thing as statement (2) but in different words, and therefore is definitely correct. ![]() Thus statement (3) is definitely correct. Statement (3) says the same thing as statement (2) because \(75\%\) of \(251\) is \(188.25\), so the minimum whole number of observations in this interval is \(189\). ![]()
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