Forty percent of seeds from maize ears carry single spikelets, and the other six

Question

Forty percent of seeds from maize ears carry single spikelets, and the other sixty percent carry paired spikelets. A seed with a single spikelets will produce an ear with single spikelets 29% of the time, while a seed with paired spikelets will produce an ear with paired spikelets 26% of the time. Consider a random sample of n = 10 seeds.

(a) What is the probability that exactly five of these seeds carry a single spikelet and produce an ear with a single spikelet?

(b) What is the probability that at least one of the ears produced by these seeds have single spikelets?

(c) Would a Poisson approximation be appropriate in either (a) or (b)? Why or why not?

Explanation / Answer

This follows a binomial distribution.

a) P(x,r)=nCr(p)^r(q)^n-r, where p is the robability of success, n is the number of trials and r is the specific number of success in n trials.

P(x=5)=10C5(0.29)^5(0.71)^5=0.093

b) P(x>=1)=1-P(x<1)=1-P(x=0)=1-0.033=0.967

c) Poisson approximation is not appropriate as n>=20, p<=0.05.

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