Question

One-sixth of the male freshmen entering a large state school come from out of state. If students are randomly assigned to dormitories, 180 in a building, what is the probability that in a given dormitory at least one-fifth of the students are from out of state?

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Answer to a math question One-sixth of the male freshmen entering a large state school come from out of state. If students are randomly assigned to dormitories, 180 in a building, what is the probability that in a given dormitory at least one-fifth of the students are from out of state?

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Hester
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111 Answers
1. Fracción de estudiantes de otro estado: \frac{1}{6}

2. Número esperado de estudiantes de otro estado en un dormitorio:
\mu = 180 \times \frac{1}{6} = 30

3. Cantidad de estudiantes para alcanzar al menos un quinto:
\frac{180}{5} = 36

4. Aproximación de la distribución binomial \(B(180, \frac{1}{6})\) a normal \(N(30, \sigma)\):

\sigma \approx 5

5. Probabilidad con \(Z\):

P(Z \geq 1.2) \approx 0.115

6. La probabilidad de que al menos un quinto de los estudiantes provenga de otro estado es:
0.115

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