Problem 1 Suppose that the bivariate data (x, y) represent the amount of hours per week worked by part-time employees in a small business (x) and the amount of a weekly pay check (y) issued to the employee. These records were summarized, and the summaries are shown below.
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VARIABLE
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SAMPLE SUMMARIES
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|
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MEAN
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STANDARD DEVIATION
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COVARIANCE
|
|
HOURS (X)
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40.00
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20.00
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576.00
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WAGES (Y)
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1,120.00
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45.00
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A. What is the correlation between x and y?
B. Determine the slope and intercept for the fitting line equation
Slope = intercept =
C. If john has worked 30 hours during the week analyzed, what his
Estimated pay check should be?
[fitted value] for john =
D. John has earned $1,140 for the week analyzed. Is his record on the scatter plot above or below the fitted line?
Determine the residual for john. [residual] for john =
[observation] is (above) or (below) the fitted line.
E. If alyssa worked 35 hours and her pay check at the end of the week was $1,075 for the week analyzed. What will her estimated pay check be?
[fitted value for alyssa] =
F. Determine the residual for alyssa.
Is her record on the scatter plot above or below the fitted line? [residual] for alyssa =
[observation] is (above) or (below) the fitted line.
Problem 2 [15 points = 5 + 5 + 5]
The number of computers sold at an appliances store has a distribution shown below.
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NUMBER OF COMPUTERS SOLD
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PROBABILITY
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0
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0.05
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1
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0.10
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2
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0.30
|
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3
|
0.25
|
|
4
|
0.20
|
|
5
|
0.10
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1. Determine the probability that the store sells at most 4 computers.
P [x ≤ 4] =
2. What is the chance to sell at least 2 computers?
P [x ≥ 2] =
3. What is the probability to sell an odd number (1, 3, or 5) of computers?
P [x = 1 or 3 or 5] =
Problem 3:
Assume that a randomly selected student has a 60% chance to pass the first intermediate exam at the level of c or higher. Two students are independently selected at random.
1. What is the chance that both of them will get c or above?
P [1st student and 2nd student will get c or above] =
2. What is the chance that exactly one student out of two will get c or above?
P [either 1st or 2nd student (and not both) will get c or above] =
3. What is the chance that at least one student will get a c or higher?
P [at least one student, 1st or 2nd (or both) will get c or higher] =
4. What is the chance that both students will get below c? P [1st and 2nd students both go below c] =