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

Age 16 to 18 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.