Suppose that, in flight, airplane engines will fail (i.e. break down) with probability 1 - p, independently from engine to engine. An airplane needs a majority of its engines operative to complete a successful
flight. (Note 1: a majority of engines operative means that more engines are working than not working;
Note 2: if 1
-
p is the probability of an engine failing, then p is the probability that the engine is working.)
a)
If p = 4/5, what is the prob
ability that a 3
-
engine plane will complete a successful flight?
b)
If p = 2/3, what is the probability that a 5
-
engine plane will complete a successful flight?
c)
What is the standard deviation of the number of working engines for a 5
-
engine plane?
d)
Suppose the
factory which manufactures the engines has undergone upgrades to improve their engines. With the upgrades engine failures only occur in 1 out of 400 engines. There are 275 newly manufactured engines waiting to be shipped. Write out the expression (do n ot solve) to
find the probability that 1 or 2 of these new engines will fail.
e)
Is there an appropriate approximation that can be used to det ermine the probability in part d
)?
Explain why or why not and then use that approximation to find this probability