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坂口友香

CADR-177 3. He became their first mayor, becoming the first Chinese American to hold that position at the time. 口 12 (a) Find the probability that a randomly chosen person’s height is less than 107.9 cm. (b) Find the probability that a randomly chosen person’s height is between 122.9 cm and 129.9 cm. (c) Find the minimum height for the tallest 87% of people. ### Solutions **a) Find the probability that a randomly chosen person’s height is less than 107.9 cm** We use the formula for the area: $$ P(X < x) = Phileft(frac{x - mu}{sigma} ight) = Phileft(frac{107.9 - 117.3}{7.2} ight) = Phileft(frac{-9.4}{7.2} ight) $$ $$ Phi(-1.306) = 0.096 $$ <center>Therefore, the probability is 0.096</center> **b) Find the probability that a randomly chosen person’s height is between 122.9 cm and 129.9 cm** We use the formula for the area: $$ P(122.9 < X < 129.9) = Phileft(frac{129.9 - 117.3}{7.2} ight) - Phileft(frac{122.9 - 117.3}{7.2} ight) = Phileft(frac{12.6}{7.2} ight) - Phileft(frac5.6}{7.2} ight) $$ $$ Phi(1.75) - Phi(0.778) = 0.9599 - 0.7803 = 0.1796 $$ <center>Therefore, the probability is 0.1796</center> **c) Find the minimum height for the tallest 87% of people** We use the formula for the area: $$ P(X > x) = 0.87 = Phileft(frac{x - mu}{sigma} ight) = Phileft(frac{x - 117.3}{7.2} ight) $$ $$ Phi(x) = 1 - 0.87 = 0.13 = Phi(-1.13) $$ $$ frac{x - 117.3}{7.2} = -1.13 = x = 117.3 - 1.13 * 7.2 = 109.164 $$ <center>Therefore, the minimum height is 109.164 cm</center>

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