Suppose that the probability that a corn seed from a certain batch does not germinate equals 0.02. If we plant 200 of these seeds, what is the probability that
• A) At most 5 seeds will not germinate?
• B) Exactly 3 will not germinate?
• C) At least 3 will not germinate?
1
Expert's answer
2022-06-01T13:08:25-0400
X∼Bin(n=200,p=0.02)
Check ifX has approximately a normal distribution with μ=np and σ=npq. .
In practice, the approximation is adequate provided that both np≥10 and nq≥10, since there is then enough symmetry in the underlying binomial
distribution.
Check
np=200(0.02)=4<10
When the value of n in a binomial distribution is large and the value of p is very small, the binomial distribution can be approximated by a Poisson distribution. If n>20 and np<5 or nq<5 then the Poisson is a good approximation.
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