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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Aim High

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### Over-booking

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Teachers' Resources

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.

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?