Comme un jeu

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

An airline knows that passengers who buy a ticket do not always show up for the flight.
For a single ticket sold, let \(X_i\) be the number of people showing up (\(1\) if they show up, \(0\) if they don't).
This variable \(X_i\) follows a Bernoulli distribution with probability of success \(p = 0.9\) (representing a 90\(\pourcent\) show-up rate).
The airline sells 160 tickets for a flight that has only 150 seats. Let \(S_{160}\) be the total number of passengers who show up.

Find the expected number of passengers who show up, \(E(S_{160})\).
Calculate the standard deviation for a single passenger (\(\sigma\)), and then find the standard deviation of the total number of passengers, \(\sigma(S_{160})\).
Can we assume the total number of passengers \(S_{160}\) is normally distributed? Explain.
Find the probability that the flight is overbooked (i.e., more than 150 passengers show up).

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