Comme un jeu

Lower Limit: Upper Limit: Mean (μ): Standard Deviation (σ):

A farmer plants seeds to grow corn. Due to soil conditions and weather, not every seed germinates (sprouts).
For a single seed planted, let \(X_i\) be the result (\(1\) if it germinates, \(0\) if it dies).
This variable \(X_i\) follows a Bernoulli distribution with probability of success \(p = 0.8\) (an 80\(\pourcent\) germination rate).
The farmer plants 1000 seeds. Let \(S_{1000}\) be the total number of seeds that germinate.

Find the expected number of seeds that germinate, \(E(S_{1000})\).
Calculate the standard deviation for a single seed (\(\sigma\)), and then find the standard deviation of the total number of germinated seeds, \(\sigma(S_{1000})\).
Can we assume the total number of germinated seeds \(S_{1000}\) is normally distributed? Explain.
The farmer has a contract to deliver at least 780 corn stalks. Find the probability that he meets this requirement (i.e., \(S_{1000} \ge 780\)).

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