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 $$\(X\)$$. State, with a justification, an approximating distribution for $$\(X\)$$, giving the values of any parameters. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_s21_qp_63 Year:2021 Question No:5(a)

Answer:

\(\operatorname{Po}(2.5)\)
\(n=25000>50\) and \(n p(\) or \(\lambda)=2.5\) which is \(<5\)
or \(n=25000>50\) and \(\mathrm{p}=0.0001<0.1\)

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.)

Solution:

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