quiz5_key - population What is P(140 ≤ ¯ Y ≤ 150...

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NAME: Stat 205 Quiz 5 The heights of a certain population of corn plants follow a normal distribution with mean μ Y = 145 cm and standard deviation σ Y = 22 cm. (a) (4 points) What percentage of plants are between 140 cm and 150 cm tall? Answer: This is P (140 Y i 150) = P ± 140 - 145 22 Y i - 145 22 150 - 145 22 = P ( - 0 . 227 Z 0 . 227) P ( Z 0 . 23) - P ( Z ≤ - 0 . 23) = 0 . 59 - 0 . 41 = 0 . 18 . Also: normalcdf(140,150,145,22). (b) (4 points) Let ¯ Y be the mean height of a random sample of n = 16 plants from the
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Unformatted text preview: population. What is P (140 ≤ ¯ Y ≤ 150) ? Answer: P (140 ≤ ¯ Y ≤ 150) = P ± 140-145 22 / √ 16 ≤ Y i-145 22 / √ 16 ≤ 150-145 22 / √ 16 ¶ = P (-. 91 ≤ Z ≤ . 91) ≈ P ( Z ≤ . 91)-P ( Z ≤ -. 91) = 0 . 82-. 18 = 0 . 64 . Also: normalcdf(140,150,145,5.5). (c) (4 points) What is P ( ¯ Y ≤ 145) = P ( ¯ Y ≤ μ Y ) ? Answer: 0.5....
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