Most plants of a certain type have three leaves. However, it is known that, on average, 1 in 10000 of these plants have four leaves, and plants with four leaves are called 'lucky'. The number of lucky plants in a random sample of 25000 plants is denoted by $$$X$$$. Use your approximating distribution to answer parts (b) and (c). Find $$$\mathrm{P}(X \leqslant 3)$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_63 Year：2021 Question No：5(b)

Answer:

$\mathrm{e}^{-2.5}\left(1+2.5+\frac{2.5^{2}}{2}+\frac{2.5^{3}}{3 !}\right)$
$0.758(3 \mathrm{sf})$

Knowledge points:

6.1.1 use formulae to calculate probabilities for the distribution $\text { Po }(\lambda)$

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.)

Answer:

Knowledge points:

Solution:

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