7. For the table that follows, answer the following questions: x y 1 -1/4 2 -1/2

Question

7. For the table that follows, answer the following questions:
x y
1 -1/4
2 -1/2
3 -3/4
4 ( )

- Would the correlation between x and y in the table above be positive or negative? - Find the missing value of y in the table. - How would the values of this table be interpreted in terms of linear regression? - If a “line of best fit” is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?

9. A bag of colored blocks contains the following assortment of colors:
red (13), blue (12), orange (21), purple (14), green (14), and yellow (6).

Construct the probability distribution for x.


10. A set of 50 data values has a mean of 25 and a variance of 36.
I. Find the standard score (z) for a data value = 31.
II. Find the probability of a data value > 31.
III. Find the probability of a data value < 31.Show all work.

Explanation / Answer

7. y decreases as x increases, so the correlation would be negative. The missing value is -1, assuming that the correlation is 1, since y decreases by 1/4 when x increases by 1. The linear regression equation would then by y = (-1/4)x and the slope would be negative. 9. The information provided does not indicate what x represents. How many blocks are you choosing? Does X represent the number of blocks of a particular color? Or the number of blocks you need to choose until you get a red one? Or...? 10. z = (31-25)/sqrt(36) = 6/6 = 1 By the Empirical Rule, P(-11) = 16% 100%-16% = 84%

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