When a pair of coils is placed around a homing pigeon and a magnetic field applied that leverses the earth's field, it is thought that the bird will become disoriented. Under these circumstances it is just as 1ikely to fly in one direction as in any other.
Let 0 denote the direction in radians of the bird's initial flight. See Fig. 4.16. 0 is uniformly distributed over the interval [0,217].
(a) Find the density for O.
(b) Sketch the graph of the density. The uniform distribution is sometimes called the "rectangular" distribution. Do you see why?
(c) Shade the area corresponding to the probability that a bird will orient within 77/4 radians of home, and find this area using plane geometry.
(d) Find the probability that a bird will orient within 17/4 radians of home by integrating the density over the appropriate region(s), and compare your answer to that obtained in part (c).
(e) If 10 birds are released independently and at least seven orient within 17/4 radians of home would you suspect that perhaps the coils are not disorienting the birds to the extent expected? Explain, based on the probability of this occurring.