Busy Phone Lines. An administrative office has eight incoming telephone lines. The probability distribution of the number of busy lines, Y , is as follows.

y 0123 4 56 78 P(Y = y) 0.033 0.124 0.202 0.214 0.1287 0.105 0.099 0.0543 0.04 Use random-variable notation to express each of the following events.

The number of busy lines is

a. exactly five.

b. at least five.

c. between two and six, inclusive.

d. at least one.

Apply the special addition rule and the probability distribution to determine

e. P(Y = 5).

f. P(Y ≤ 5).

g. P(1 ≤ Y ≤ 6). h. P(Y ≥ 1).