It is known that, on average, 1 in 300 flowers of a certain kind are white. A random sample of 200 flowers of this kind is selected. The probability that a randomly chosen flower of another kind is white is $$\(0.02\)$$. A random sample of 150 of these flowers is selected. Use an appropriate approximating distribution to find the probability that the total number of white flowers in the two samples is less than 4. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_63 Year：2020 Question No：1(c)
Answer:
\(\operatorname{Po}\left(\frac{11}{3}\right)\)
\(e^{-\frac{11}{3}}\left(1+\frac{11}{3}+\frac{\left(\frac{11}{3}\right)^{2}}{2 !}+\frac{\left(\frac{11}{3}\right)^{3}}{3 !}\right)\)
\(=0.501 \quad(3 \mathrm{sf})\)
\(e^{-\frac{11}{3}}\left(1+\frac{11}{3}+\frac{\left(\frac{11}{3}\right)^{2}}{2 !}+\frac{\left(\frac{11}{3}\right)^{3}}{3 !}\right)\)
\(=0.501 \quad(3 \mathrm{sf})\)
Knowledge points:
6.1.4 use the Poisson distribution as an approximation to the binomial distribution where appropriate (The conditions that n is large and p is small should be known; n > 50 and np < 5, approximately.)
6.2.1.6 if and have independent Poisson distributions then X + Y has a Poisson distribution. (Proofs of these results are not required.)
Solution:
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