Comme un jeu

Probability (0 to 1): Mean (μ): Standard Deviation (σ):

A shuttle bus service transports passengers from a hotel to the airport. The hotel has received \(n=50\) booking requests.
The number of passengers per booking, \(X_i\), can be \(1, 2,\) or \(3\) people with probabilities \(0.5, 0.3,\) and \(0.2\) respectively.
Assume that the size of each booking group is independent.
Let \(S_{50}\) be the total number of passengers.

Find the mean \(\mu\) and the variance \(\sigma^2\) of the number of passengers for a single booking.
Find the expected total number of passengers \(E(S_{50})\) and the standard deviation of the total \(\sigma(S_{50})\).
Can we assume \(S_{50}\) is normally distributed? Explain.
The bus company wants to be \(90 \pourcent\) confident that they have enough seats. What should be the minimum capacity of the bus (find \(k\))?

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.