(3.12. C.13. C14. The grade-point average in an econometrics examination was normally dis- tributed with a mean of 75. In a sample of 10 percent of students it was found that the grade-point average was greater than 80. Can you tell what the s.d. of the grade-point average was? The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and an 5d. of 0.8 ounces. The cost of producing each tube is 50 cents. If in a quality control examination a tube is found to weigh less than 6 ounces, it is to be relled to the mean value at a cost of 20 cents per tube. On the other hand, if the tube weighs more than 7 ounces, the company loses a prot of 5 cents per tube. If 1000 tubes are examined, a. How many tubes will be found to contain less than 6 ounces? b. In that case, what will be the total cost of the rell? c. How many tubes will be found to contain more than 7 ounces? In that case, what will be the amount of prots lost? If X ~ N(10, 3) and Y ~ N(15, 8), and if X and Y are independent, what is the probability distribution of a.X+Y b. XY c.3X d. 4X+5Y