Σ(- x i 1 9. Find the variance. Hint: S x п—1 10. Prove that when exam scores are weighted equally, the weighted mean is the same as the mean. 1.e. P n Σ. when scores are weighted equally XWi п i=1 i=1 n 11. The mean SAT (Scholastic Aptitude Test) score is 900 with a standard deviation of 200. According Chebyshev's Theorem at least what proportion of scores are between (a) 700 and 1100? (b) 500 and 1300? (c) 300 and 1500? п 12. Prove that the sum of the deviations from the mean is zero. i.e. Prove that (x- x) = 0. i-1 13. Use the following equation predicting pounds of garbage based on the number of people in the hou garbage = 10 household size+ 15 (a) Identify and interpret the slope. (b) Identify and interpret the intercept. (c) Find the residual of a household with 3 people which discarded 40 pounds of garbage. (d)Fill in the blank: The least squares linear regression line minimizes 14. One study showed a strong positive correlation between the number fire trucks sent to a fire and t

Please help me answer the following questions. Thank you

Mr. Imperfecto teaches another math class.  This time he has 23 students take a test, the average score on which is an 87.  Mr. Imperfecto realizes he put the wrong grade in for a student.  He entered a 35, and the score should have been an 85.  To the nearest integer, what is the new class average?

2. If 4 times a number is added to 5, the result is 35 more than the number. Find the number.