(1 point) Suppose there are three sections of a Statistics course taught by the same instructor. The class averages for each section on Test 1 are displayed in the table below.Class Size Class AverageSection 01 22 77Section 02 27 76Section 03 16 85

A statistic professor is investigating the relationship between tutorial class size and academic performance for a post-graduate statistics for business and economics course. She collects data on the tutorial class size (number of students) and average class mark (out of 100) for a sample of 15 tutorial classes. Tutorial size (X) 15 25 22 12 28 22 17 29 8 15 22 19 21 27 15 Average mark (Y) 78 67 69 79 58 65 72 61 82 73 68 70 70 65 77 Note: you can use Excel to run a regression. Insert the above data in Excel and then click on Data/Data Analysis/Regression (a) Assuming a linear relationship between X and Y, the professor used the least-squares method and found that the Y intercept (b0) = 91.1918 and the slope (b1) = -1.0568. Interpret the meaning of the slope. Answer: for each additional student in a tutorial class, the average (tutorial) class mark is estimated to decrease by around 1.06 points, on average. Note: the word “average” is written twice because the unit of measurement of the dependent variable (Y) is average mark. The slope coefficient indicates the average change in Y associated with a one-unit change in X. (b) Predict the mean value of Y for X = 16, and interpret it

The average of a class is 30 years. 6 new students with an average age of 24 years join the class, there by increasing the average by half year find the original strength of the class.*1 point60585466

On a recent quiz about averages, the following information is known:• There were three questions on the quiz.• Each question was worth 1 mark.• Each question was marked either right or wrong (no part marks).• 50% of the students got all 3 questions correct.• 5% of the students got no question correct.• The class average mark was 2.3 out of 3.Determine the percentage of students who got exactly 1 question correct and thepercentage of students who got exactly 2 questions correct.

If the average marks of two batches of 55 and 45 students respectively is 50 and 60, then the average marks of all the students is:a.54.5b.55c.56.8d.53

Emily, a teacher, was calculating the test scores of her class, which consisted of 50 students. Initially, she calculated the class average to be 75. However, upon inspection, she discovered that scores 90 and 65 were mistakenly noted as 80 and 60. What is the correct class average (up to one decimal place) after rectifying these mistakes?