Cherry trees in a certain orchard have heights that are normally distributed with a mean μ = 117 inches and a standard deviation σ = 11 inches. Use the Cumulative Normal Distribution Table to answer the following: (a) Find the 22nd percentile of the tree heights. (b) Find the 88th percentile of the tree heights. (c) Find the third quartile of the tree heights. (d) An agricultural scientist wants to study the tallest 1% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this? Round the answers to at least two decimal places.
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22. Using the Cumulative Normal Distribution Table, we find that the closest value is 0.2219, which corresponds to a z-score of -0.76. Now, we can use the z-score formula to find the height: z = (x - μ) / σ x = z * σ + μ x = -0.76 * 11 + 117 x ≈ 104.64 So, the Show more…
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Cherry trees in a certain orchard have heights that are normally distributed with mean =109 inches and standard deviation =11 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 23rd percentile of the tree heights. (b) Find the 81st percentile of the tree heights. (c) Find the second quartile of the tree heights. (d) An agricultural scientist wants to study the tallest 2% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this?
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