Assignment:
A certain factory has three machines A,B and C that produces one type of light bulbs.Past experience has shown that the lifetime of a light bulb by machine A can be modeled as an exponential random variable with an average of 20 days, whereas the lifetime of a bulb produced by a machine B can modeled as a normal random variable with mean of 15 days and variance of 5.76(days^2).As for the light bulbs produced by machine C, they usually last anywhere between 13 to 17 days.It is further known that 30% of the factory production of this type of light bulbs comes from machine A and 50% of production comes from machine B.Suppose all the light bulbs after production are packaged identically and stored in the same storage room.
a) A bulb is selected at random from the storage room and tested.Find the probability that the bulb was produced by machine C given that it was still operating after 16 days.
b) A random sample of size 10 bulbs is selected from the storage room, what is the probability that exactly 4 of the bulbs will have a lifetime less than 16 days?
c) On average ,how many bulbs must be selected in order to get 7 bulbs with a lifetime between two and three weeks?
d) Find the expacted lifetime of a lifetime of a light bulb produced by this factory.
Provide complete and step by step solution for the question and show calculations and use formulas.