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In a large population, 73% of the population are short-sighted. A samples of 7 people is randomly chosen from the population. A random sample of n people is chosen instead from the same population. Find the minimum number n such that there is at least 99% chance of having one or more people who are short-sighted

Respuesta :

Answer:

4

Step-by-step explanation:

Let x , be the number of short sighted people among n people.

[tex]x_{1}[/tex], follows binomial distribution : x∼B(N, 0.73)

[tex]\geq[/tex]0.99

1-p([tex]x_{1}[/tex][tex]\geq[/tex]1)[tex]\geq[/tex]0.99

1-0.99[tex]\geq[/tex]p([tex]x_{1}[/tex]=0)

p([tex]x_{1}[/tex]=0)[tex]\leq[/tex]0.01

[tex]{n}_C_{0}[/tex] × [tex]0.73^{0}[/tex]×[tex]0.27^{n}[/tex][tex]\leq[/tex]0.01

[tex]0.27^{n}[/tex][tex]\leq[/tex] 0.01

nln0.27[tex]\leq[/tex]ln0.01

n[tex]\geq[/tex]ln0.01/ln0.27

n[tex]\geq[/tex]3.52 ≈ 4

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