The number of accidents on a certain road has a Poisson distribution with mean $$\(0.4\)$$ per 50-day period. The probability that there will be no accidents during a period of $$\(n\)$$ days is greater than $$\(0.95\)$$. Find the largest possible value of $$\(n\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_62 Year：2020 Question No：4(b)
Answer:
\(\mathrm{e}^{-\lambda}>0.95\)
\(-\lambda>\ln 0.95\) or \(\lambda<0.051293\) OE
\(' 0.051293 ' \times 50 \div 0.4(=6.411)\)
Largest \(n\) is \(6(3 \mathrm{sf})\)
Allow \(n=6\) or \(n \leqslant 6\) (NOT \(n<6\) or \(n \geqslant 6\) as final answer)
\(-\lambda>\ln 0.95\) or \(\lambda<0.051293\) OE
\(' 0.051293 ' \times 50 \div 0.4(=6.411)\)
Largest \(n\) is \(6(3 \mathrm{sf})\)
Allow \(n=6\) or \(n \leqslant 6\) (NOT \(n<6\) or \(n \geqslant 6\) as final answer)
Knowledge points:
6.1.1 use formulae to calculate probabilities for the distribution $\text { Po }(\lambda)$
Solution:
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