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The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Into the Normal Distribution

Investigate the normal distribution

Normal Intersection

Explore the intersection possibilities for normal pdfs.

Aim High

Age 16 to 18
Challenge Level

For the second part you will need to use the formula for the expected value of a random variable $X$:
$$E(X) = \int^\infty_{-\infty} xf(x) dx$$

Don't forget that you can split an integral into two parts
$$\int^\infty_{-\infty} xf(x) dx=\int^a_{-\infty} xf(x) dx+\int^\infty_a xf(x) dx$$

You might also want to use the Erf function in Excel to work out the numbers and to change variables in any integrals to reduce them to standard $N(0,1)$ cases.