19. On a particular farm, profit depends on rainfall. The rainfall is normally distrib-

uted with a mean of 31 cm and a standard deviation of 9 cm. Farm profits are:

a)

$100,000 if rainfall is over 44 cm,

b)

$150,000 if rainfall is between 29 and 44 cm,

c)

$130,000 if rainfall is between 22 and 29 cm,

d)

$ 65,000 if rainfall is between 15 and 22 cm, and

e)

-$ 80,000 if rainfall is less than 15 cm

Find the expected farm profit.