Suppose the mean gpa of all students graduating from a particular university in 1975 was 2.30. the registrar plans to look at records of students graduating last year to see if the mean gpa has increased. define notation and state the null and alternative hypotheses for this investigation.

The following data pertains to activity and costs for two months: june july activity level in 10,000 12,000 direct materials $16,000 $ ? fixed factory rent 12,000 ? manufacturing overhead 10,000 ? total cost $38,000 $42,900 assuming that these activity levels are within the relevant range, the manufacturing overhead for july was: a) $10,000 b) $11,700 c) $19,000 d) $9,300

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

The returns on the common stock of maynard cosmetic specialties are quite cyclical. in a boom economy, the stock is expected to return 22 percent in comparison to 9 percent in a normal economy and a negative 14 percent in a recessionary period. the probability of a recession is 35 percent while the probability of a boom is 10 percent. what is the standard deviation of the returns on this stock?