A plane lands or takes off, on average once per 45 seconds at an airfield. Calculate what is the probability that in a random selected hour we notice:

Question

1) At least 75 landings or take offs?

2) Under 100 landings or take offs?

Answer 1

This is a job for the Poisson distribution,

followed by the normal distribution approximation

to the Poisson.

The mean number per hour is

mu = (1/45 s) (3600 s/hr) = 80 and\

the population std dev is

sigma = sqrt(mu) = 8.9.

Large N>>1 allows using the normal distribution approximation

z >= (75-80)/8.9 = -0.56

N(0, 1; -0.56) = 0.71

71% larger than this 75 value

Fewer than 100?

z = (100-80)/8.9 = 0.22

22% larger and 78% smaller.than this 100 value