Problem # 2 g 12.5 Hts}. Fifty-one percent of U.S college graduates consider themselves underemployed. You randomly select 250 US. college graduates an ask them whether they consider themselves underemployed. Find the probability that the number who consider themselves undercmploycd is: a) No more than 125 b) Between 100 and 125 inclusive Problem # 8 (12.5 pts]. (Draw the bell curves for each question). Procter 8.: Gamble reported that an American family of four washes and average of 1 ton (2000 pounds) of clothes each year. If the standard deviation is 195.2 pounds, nd the following probabilities: a) That the mean of a randomly selected sample of 52 families of four will be between 1985 and 1992 pounds. b) That the mean of a randomly selected sample of 50 families of four Problem # 3 (12.5 pts) The following table shows the percentage of the vote predicted by a poll for eleven candidates for the U.S Senate in different states, x, and the corresponding percentages of the vote that they actually received, y: Poll (x) 42 34 59 41 53 40 55 44 41 52 42 Election 51 31 56 42 58 35 54 42 41 54 56 (y) a) Find the correlation coefficient r b) find the regression equationProblem # 4 [12.5 Hts} (Draw the bell curves for each question). The average teacher's salary in Connecticut (ranked rst among states) is $57,331 Suppose that the distribution of salaries is normally distributed with a standard deviation of $7000. a) What is the probability that a randomly selected teacher makes more than $52000 per year? b) If we sample 100 teacher's salaries, what is the probability that the sample mean is between $52000 and $56,650 per year? Problem # 5 ( 12.5 pts). Eighty-five percent of U.S civilian full-time employees have access to medical care benefits. You randomly select nine civilian full-time employees. Find the probability that the number of civilian full-time employees who have access to medical care benefits is a) Exactly six 6 b) At least sixProblem # 6 (12.5 pts) The average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 17 different brands of 1- ounce chocolate chip cookies resulted in the following calorie amounts. At the a = 0.05 level, is there sufficient evidence that the average calorie content is equal to 110 calories? 100 126 151 160 184 125 154 145 100 160 150 140 138 120 110 145 126Problem # 7 [ 12.5 pts}. In the following table 277 college students are classied according to their class standing and also according to their favorite pizza topping: Anchovies Chicken Onions Hamburger Pineapple Total , (II) (E) Freshman 12 14 15 12 10 63 (F) Sophomore l 7 2 l 0 14 23 75 (5} Junior (J) 18 22 13 15 17' 85 Senior (R) 9 13 16 7 9 54 Total 56 7'0 44 48 59 277' If one of these students is selected at random, nd the following probabilities: a) The probability that the student likes Chicken or Hamburger topping given that the student is a junior or a senior. Problem # 1 ( 12.5 pts). To test the durability of a new paint for white center lines, a highway department painted test strips across heavily traveled roads in sixteen different locations, and electronic counters showed that they deteriorated after having been crossed by 12.58 14.26 16.78 13.65 11.5 10.83 12.64 13.37 16.20 14.96 13.5 13.1 14.92 15.66 10.83 and 14.87 million cars. Construct a 95% confidence interval for the average amount of traffic (car crossings) this paint can withstand before it deteriorates