p$.175$#$63$

A consumer is trying to decide between two long$-$distance calling

plans. The first one charges a flat rate of $10$ cents per minute,

whereas the second charges a flat rate of $99$cents for calls up to

$20$ minutes in duration and then $10$cents for each additional

minute exceeding $20($assume that calls lasting a non$-$integer

number of minutes are charged proportionately to a whole$-$minute's

charge$).$ Suppose the consumer's distribution of call duration is

exponential with parameter lambda.depend on what the expected call duration is$.$