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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?
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.
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.