The probability distribution for damage claims paid by the newton automobile insurance company on collision insurance follows.
payment ($) probability0 0.85500 0.041,000 0.043,000 0.035,000 0.028,000 0.0110,000 0.01a. use the expected collision payment to determine the collision insurance premium that would enable the company to break even. if required, round your answers to two decimal places. b. the insurance company charges an annual rate of $520 for the collision coverage. what is the expected value of the collision policy for a policyholder? if required, enter negative value as negative number. why does the policyholder purchase a collision policy with this expected value?

Areal estate agent is considering changing her cell phone plan. there are three plans to choose from, all of which involve a monthly service charge of $20. plan a has a cost of $.42 a minute for daytime calls and $.17 a minute for evening calls. plan b has a charge of $.52 a minute for daytime calls and $.15 a minute for evening calls. plan c has a flat rate of $80 with 275 minutes of calls allowed per month and a charge of $.38 per minute beyond that, day or evening.a. determine the total charge under each plan for this case: 150 minutes of day calls and 70 minutes of evening calls in a month. (do not round intermediate calculations. round your answer to 2 decimal places. omit the "$" sign in your response.)c. if the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (round each answer to the nearest whole number.include the indifference point itself in each answer.)d. suppose that the agent expects both daytime and evening calls. at what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans a and b?