Question

The phone lines to an airline reservation system are occupied 40% of the time Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. What is the probability that for exactly three calls the lines are occupied? ABILITY DISTRIBUTIONS What is the probability that for at least one call the lines are not occupied? What is the expected number of calls in which the lines are all occupied?

Answer 1

Answer:

0.215 ,10,  4

Step-by-step explanation:

Let X be the random variable of number of calls (out of total of 10 calls) during which the phone lines were occupied. X has the binomial distribution with parameters n = 10, p = 0.4.  

P(X = 3) = (10 3)*0.4^3*0.67^7 = 0.215  

P(X $\leq$ 9) = 1 — P(X > 9) = 1 — P(X = 10) =

             = 1 — (10 10)*0.41^10*0.6^0

             = 10  

E(X) = n x p = 10 x 0.4

                   = 4