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show all your work. indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation.

a simple random sample of adults living in a suburb of a large city was selected. the age and annual income of each adult in the sample were recorded. the resulting data are summarized in the table below.

annual income
age category $25,000_$35,000 $35,001_$50,000 over $50,000 total
21_30 8 15 27 50
31_45 22 32 35 89
46_60 12 14 27 53
over 60 5 3 7 15
total 47 64 96 207

a) what is the probability that a person chosen at random from those in this sample will be in the 31_45 age category? 89/207=0.43
b) what is the probability that a person chosen at random from those in this sample whose incomes are over $50,000 will be in the 31_45 age category? show your work.35/96=0.36
c) based on your answers to (a) and (b), is annual income independent of age category for those in this sample? explain.

10. the following table is the assignment of probabilities that describes the age (in years) and the gender of a randomly selected american student.

age 14_17 18_24 25_34 +35
male 0.01 0.30 0.12 0.04
female 0.01 0.30 0.13 0.09

a) what is the probability that the student is female? 0.53/100=0.0053
b) what is the probability that the student is age 25_34? 0.25/100=0.0025
c) what is the probability that the student is either male or at least 35 years old?
d) what is the probability that the student is at least 35 years old? 0.04/0.47=0.085
e) are being a female and being at least 35 years old independent events? provide statistical reasoning for your answer.

1. descriptive statistics quickly describe large amounts of data can predict future stock returns with surprising accuracy statisticians understand non-numeric information, like colors refer mainly to patterns that can be found in data 2. a 15% return on a stock means that 15% of the original purchase price of the stock returns to the seller at the end of the year 15% of the people who purchased the stock will see a return the stock is worth 15% more at the end of the year than at the beginning the stock has lost 15% of its value since it was originally sold 3. a stock purchased on january 1 cost $4.35 per share. the same stock, sold on december 31 of the same year, brought in $4.75 per share. what was the approximate return on this stock? 0.09% 109% 1.09% 9% 4. a stock sells for $6.99 on december 31, providing the seller with a 6% annual return. what was the price of the stock at the beginning of the year? $6.59 $1.16 $7.42 $5.84

Cardinal company is considering a project that would require a $2,725,000 investment in equipment with a useful life of five years. at the end of five years, the project would terminate and the equipment would be sold for its salvage value of $400,000. the company’s discount rate is 14%. the project would provide net operating income each year as follows: sales $2,867,000 variable expenses 1,125,000 contribution margin 1,742,000 fixed expenses: advertising, salaries, and other fixed out-of-pocket costs $706,000 depreciation 465,000 total fixed expenses 1,171,000 net operating income $571,000 1. which item(s) in the income statement shown above will not affect cash flows? (you may select more than one answer. single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. any boxes left with a question mark will be automatically graded as incorrect.) (a)sales (b)variable expenses (c) advertising, salaries, and other fixed out-of-pocket costs expenses (d) depreciation expense 2. what are the project’s annual net cash inflows? 3.what is the present value of the project’s annual net cash inflows? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.) 4.what is the present value of the equipment’s salvage value at the end of five years? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.) 5.what is the project’s net present value? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.)

Mauro products distributes a single product, a woven basket whose selling price is $15 and whose variable expense is $12 per unit. the company’s monthly fixed expense is $4,200. required: 1. solve for the company’s break-even point in unit sales using the equation method. 2. solve for the company’s break-even point in dollar sales using the equation method and the cm ratio. (do not round intermediate calculations. round "cm ratio percent" to nearest whole percent.) 3. solve for the company’s break-even point in unit sales using the formula method. 4. solve for the company’s break-even point in dollar sales using the formula method and the cm ratio. (do not round intermediate calculations. round "cm ratio percent" to nearest whole percent.)