2. The following data represent the observed number of defective disks produced each hour based on observing the system for 30 successive hours. 5 2 2 5 3 3 3 5 6 8 0 1 0 7 6 9 5 1 7 5 3 4 6 1 2 4 4 3 a. Plot a frequency histogram for the numbers of failures per hour. b. Compute the mean and the variance of the sample. Use the formulas X =-£Xi, E x} – nX² n - (Note: You can streamline the calculations by grouping the data first, as there are only 10 distinct values.) c. If the number of defective disks produced hourly is normally distributed with mean and variance computed in part (b), determine the probability that fewer than five defectives are observed in any particular hour. d. If each disk costs the company $5 to produce and defective disks are discarded, how long (in an expected-value sense) would it take to pay off a new piece of equipment costing $45,000 that would reduce defectives to half of the current level? Assume 40-hour production weeks and 48 weeks per year.

The data show the population (in thousands) for a recent year of a sample of cities in South Carolina. 19 19 25 19 69 25 28 12 25 28 14 34 92 16 13 10 19 27 112 40 22 44 115 37 38 53 Send data to Excel Part: 0 / 8 Part 1 of 8 th The data value corresponds to the 46" percentile.

%3D For the relation Y= 12-4 X between X and Y; if standard deviation of X, o, =5 then, variance of Y will be Select one: O 100 O 400 O 20 O 200

Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births x per one thousand people in the population and the female life expectancy y (in years) are given. These data are displayed in the Figure 1 scatter plot. Birthrate, x (number of births per 1000 pop.) 16.5 35.3 39.8 17.7 30.1 27.0 13.4 47.2 49.6 49.8 48.0 24.5 Send data to calculator Female life expectancy, y (in years) 76.0 66.6 65.7 74.1 64.1 71.7 72.0 56.7 54.4 57.7 63.6 74.5 Send data to Excel Female life expectancy (in years) 85. Figure 1 80- 75- 70. 65. 60 55 50 15 20 25 30 35 40 45 50 55 Birthrate (number of births per 1000 pop.) The value of the sample correlation coefficient r for these data is approximately - 0.909. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) What is the value of the…