Comme un jeu

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

A hotel organizes a conference in a hall that has a maximum capacity of 200 seats.
To ensure the hall is full, they send out 220 invitations. Let \(X_i\) be the attendance of a single invited person (\(1\) if they attend, \(0\) if they don't).
This variable \(X_i\) follows a Bernoulli distribution with probability of success \(p = 0.85\) (representing an 85\(\pourcent\) attendance rate).
Let \(S_{220}\) be the total number of guests who attend the conference.

Find the expected number of guests, \(E(S_{220})\).
Calculate the standard deviation for a single guest (\(\sigma\)), and then find the standard deviation of the total number of guests, \(\sigma(S_{220})\).
Can we assume the total number of guests \(S_{220}\) is normally distributed? Explain.
Find the probability that there are not enough seats (i.e., more than 200 guests show up).

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