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Consider the data in Exercise 1.5 on page 13. Compute the sample variance and the sample standard deviation for both control and treatment groups. Reference Exercise 1.5: Twenty adult males between the ages of 30 and 40 participated in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control group, and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The following data show the reduction in cholesterol experienced for the time period for the 20 subjects: Control group: 7 3 -4 14 2 522 -7 95 Treatment group: -6 5 9 4 4 12 37 5 3 3 (a) Do a dot plot of the data for both groups on the same graph. (b) Compute the mean, median, and 10% trimmed mean for both groups. (c) Explain why the difference in means suggests one conclusion about the effect of the regimen, while the difference in medians or trimmed means suggests a different conclusion.5.9 A metallurgical engineer is considering two mate- rials for use in a space vehicle. All estimates are made. (a) Which should be selected on the basis of a present worth comparison at an interest rate of 12% per year? (b) At what first cost for the mate- rial not selected above will it become the more economic alternative? Material X Material Y First cost, $ -15,000 -35,000 Maintenance cost, $ per year -9.000 -7,000 Salvage value, $ 2,000 20,000 Life, years 5Because you are thankful for what you learned in engineering economy, you plan to start a perma- nent scholarship fund in the name of the professor who taught the course. You plan to deposit money now with the stipulation that the scholarships be awarded beginning 12 years from now (which happens to be the exact time that your daughter plans to begin college). The interest that is accu- mulated between now and year 12 is to be added to the principal of the endowment. After that, the in- terest that is earned each year will be awarded as scholarship money. If you want the amount of the scholarships to be $40,000 per year, how much must you donate now if the fund earns interest at a rate of 8% per year?An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by f(x) = [3r, r>1, elsewhere. (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 4 micrometers? Show that the n pieces of information in _ (x - ?) are not independent; that is, show that 2(n- 1) =0An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of 7, the number of years to maturity for a randomly selected bond, is t 3); (c) P(1.4 2).The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function 20.000 f(x) = (x+100) I>0, 0 , elsewhere. Find the probability that a bottle of this medicine will have a shell life of (a) at least 200 days; (b) anywhere from 80 to 120 days.Assume an engineering company borrows $100,000 at 10% per year compound interest and will pay the principal and all the interest after 3 years. Compute the annual interest and total amount due after 3 years. Graph the interest and total owed for each year, and compare with the previous example that involved simple interest