1. The number of television viewing hours per household and the prime viewing times are two factors that affect advertising income. A random sample of 20 households in a particular viewing area produced the following estimates of viewing hours per household: 3.0 6.0 7.5 15.0 6.5 8.0 4.0 5.5 7.5 5.0 10.0 8.0 3.6 12.0 1.0 3.5 9.0 2.0 6.5 1.0 Find the value of the following: A. Range B. variance using the computational formula C. variance using the definitional formula D. standard deviation: 2. Using the following data 3, 6, 2, 1, 7, & 5, compute the population standard deviation using any formula. A. add 2 to each of the numbers and recompute the population standard deviation. B. subtract 2 from each of the numbers and recompute the population standard deviation. C. multiply each of the numbers by 2 and recompute the population standard deviation. D. divide each of the numbers by 2 and recompute the population standard deviation. E. What happens to the standard deviation when you add, subtract, multiply, and divide the set of observations by a constant. Generalize your answer.3. A laboratory technician studied recent measurements made with two different instruments. The first measured the diameter of a ball bearing and obtained mean of 4.96mm with a standard deviation of 0.022mm. The second measured the diameter of a metal rod and obtained a mean of 6.48mmwith a standard deviation of 0.032 mm. Which of the two instruments was relatively more precise? 4. Different typing skills are required for secretaries depending on whether one is working in a law office, on an accounting firm, or for a mathematical research group at a major university. In order to evaluate candidates for these positions, an agency administers 3 distinct standardized typing samples. A time penalty has been incorporated into the scoring of each sample based on the number of typing errors. The mean and standard deviation for each test, together with the scores achieved by Mary, an applicant, are given in the following table. Sample Mary's Score Mean Standard Deviation Law 141 sec 180 sec 30 sec Accounting 7 min 10 min 2 min Math 33 min 26 min 5 min Research Where do you think should Mary be placed