Question

The probbability of having a head cold is 5% and 1000 people are checked at random what is the probability that at least 60 people have head colds?

Answer 1

# Question # 10994

The probability of having a head cold is 5% and 1000 people are checked at random what is the probability that at least 60 people have head colds? .

Solution. Clearly the number of people $X$ out of 1000 having cold has Bernoulli distribution $Bin(0.05, 1000)$, hence $P(X > 60) = P\left(\frac{X - 0.05 \cdot 1000}{\sqrt{1000 \cdot 0.05 \cdot 0.95}} > \frac{60 - 0.05 \cdot 1000}{\sqrt{1000 \cdot 0.05 \cdot 0.95}}\right) \approx 1 - \Phi\left(\frac{60 - 0.05 \cdot 1000}{\sqrt{1000 \cdot 0.05 \cdot 0.95}}\right) \approx 0.22$

Answer 0.22

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