03:51:00
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>
9月17日2008年
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