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for any given flight, an airline tries to sell as many tickets as possible. suppose that on average, 10% of ticket holders fail to show up, all independent of one another. knowing this, an airline will sell more tickets than there are seats available, and hope that there is a sufficient number of ticket holders who do not show up to compensate for its overbooking. using the central limit theorem, determine n, the maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane. use the 1/2-value-correction (called de moivre-laplace approximation) in your calculation.

Sagot :

The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 324.

The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 326.   This is calculated using the 1/2-value correction (de Moivre-Laplace Approximation). The 1/2-value correction assumes the normal distribution is symmetric, with the mean in the middle of the distribution. This means that the probability of being above the mean is equal to the probability of being below the mean.  Since the airline wants to be 99% confident that all ticket holders who do show up will be able to board the plane, this means that the airline needs to sell enough tickets such that the probability of being above the mean (300 tickets sold) is 99%.   Using the 1/2-value correction, the airline needs to sell 326 tickets to achieve this confidence level.

This is calculated as follows:   P(x > 300) = 0.99  P(x < 300) = 0.01  Using the 1/2-value-correction:

P(x = 300 + 0.5) = 0.99

Therefore,   x = 300 + 0.5=>  x = 300.5 => x = 326

To know more  confidence level refers to the  link   brainly.com/question/13242669

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