On average, 1 in 75000 adults has a certain genetic disorder. In a random sample of $$\(n\)$$ people, where $$\(n\)$$ is large, the probability that no-one has the genetic disorder is more than $$\(0.9\)$$. Find the largest possible value of $$\(n\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_61 Year：2021 Question No：5(b)
Answer:
\(\lambda=\frac{n}{75000}\)
\(\mathrm{e}^{-\frac{n}{75000}}>0.9\)
\(-\frac{n}{75000}>\ln 0.9 \quad[n<7902.04]\)
Largest value of \(n\) is 7902
Alternative method for Question 5(b)
\( \begin{array}{l}
\mathrm{e}^{-\mu}>0.9 \\ -\mu>\ln 0.9 \quad[\mu<0.10536] \\ n=\mu \times 75000
\end{array} \)
Largest value of \(n\) is 7902
Alternative method for Question \(5(b)\)
\(\frac{74999}{75000}\)
\(\left(\frac{74999}{75000}\right)^{n}>0.9\)
\(n \ln \frac{74999}{75000}>\ln 0.9\)
Largest value of \(n\) is 7901
\(\mathrm{e}^{-\frac{n}{75000}}>0.9\)
\(-\frac{n}{75000}>\ln 0.9 \quad[n<7902.04]\)
Largest value of \(n\) is 7902
Alternative method for Question 5(b)
\( \begin{array}{l}
\mathrm{e}^{-\mu}>0.9 \\ -\mu>\ln 0.9 \quad[\mu<0.10536] \\ n=\mu \times 75000
\end{array} \)
Largest value of \(n\) is 7902
Alternative method for Question \(5(b)\)
\(\frac{74999}{75000}\)
\(\left(\frac{74999}{75000}\right)^{n}>0.9\)
\(n \ln \frac{74999}{75000}>\ln 0.9\)
Largest value of \(n\) is 7901
Knowledge points:
6.1.1 use formulae to calculate probabilities for the distribution $\text { Po }(\lambda)$
Solution:
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