Chemistry class had two exams. on the first exam the mean score was 70 with a standard deviation of 10. on the second exam the mean score was 60 with a standard deviation of 15. the correlation coefficient between the scores of the two exams was r = 0.6. we run a regression analysis with the first exam score as the independent variable and the second exam score as the dependent variable. we use the result to estimate the score on the second exam for each student based on their score on the first exam. for at least 75% of the students in the class, the regression estimated score for the second exam will be correct to within how many points?

60% correction

Step-by-step explanation:

From the given data,

Let xb = 70 (first exam score mean)

yb = 60 (second exam score mean)

σx = 10 (standard deviation of first exam)

σy = 15 (standard deviation of second exam)

ε = 0.6

From regression equation y = βo + β1*x

and β1 = ε * σy/σx

= 0.6 * 15 / 10 = 0.9

Also, βo = yb - β1*xb

Substituting the values to the equation,

βo = -3

Hence y = -3 + 0.9x

For x = 75 (supposing a student gets 75 in first exam to calculate second exam score), we have y = 64.5

Hence, ε = 0.6 means we have about a 60% dependency between the exam scores, so 60% point's corrects the second exam scores

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt