### Over-booking

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

### Aim High

How do you choose your planting levels to minimise the total loss at harvest time?

# Normal Intersection

##### Stage: 5 Challenge Level:

Imagine that I plot the pdfs for two normal distributions on the same axes. Could I choose the parameters so that the curves intersect $0$, $1$ or $2$ times?

Imagine that I plot the cdfs for two normal distributions on the same axes. Could I choose the parameters so that the curves intersect $0$, $1$ or $2$ times?

Imagine that I plotted the pdf and the cdf of normal distribution on the same axes. Would they always, sometimes or never intersect?

Give examples or convincing arguments to support your reasoning. You might want to experiment with specific choices of parameters before attempting to construct more general arguments.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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