Let x1, be independent and identically distributed random variables, each with expected value ? = e[xi] = 2 and variance \sigma ^2 = var(xi) = 4. find an upper bound for p(x1+x2+···+x144 > 144) using the following steps:

(a) let z=x1+ x2++x144, and use rules of expectation and variance to find e[z]and var[z].
(b) let a be the difference between 144 and e[z].
(c) apply chebychev's inequality to z using the number a.
(d) use the fact that z is symmetrically distributed about its mean to connect your answer to (c) to the original question. (hint: draw a symmetric density curve for z, and mark the values e[z], (e[z]+a) and (e[z]? a.)
label regions in the graph with their corresponding probabilities.)

Highland company produces a lightweight backpack that is popular with college students. standard variable costs relating to a single backpack are given below

Exercise 18-15 sheffield appliance center is an experienced home appliance dealer. sheffield appliance center also offers a number of services for the home appliances that it sells. assume that sheffield appliance center sells ovens on a standalone basis. sheffield appliance center also sells installation services and maintenance services for ovens. however, sheffield appliance center does not offer installation or maintenance services to customers who buy ovens from other vendors. pricing for ovens is as follows. oven only $790 oven with installation service 850 oven with maintenance services 970 oven with installation and maintenance services 990 in each instance in which maintenance services are provided, the maintenance service is separately priced within the arrangement at $180. additionally, the incremental amount charged by sheffield appliance center for installation approximates the amount charged by independent third parties. ovens are sold subject to a general right of return. if a customer purchases an oven with installation and/or maintenance services, in the event sheffield appliance center does not complete the service satisfactorily, the customer is only entitled to a refund of the portion of the fee that exceeds $790. assume that a customer purchases an oven with both installation and maintenance services for $990. (b) indicate the amount of revenue that should be allocated to the oven, the installation, and to the maintenance contract.

An investment offers a total return of 18 percent over the coming year. janice yellen thinks the total real return on this investment will be only 14 percent. what does janice believe the inflation rate will be over the next year?