Problem 1 :
The scatter plot below indicates which of the following.
a) positive correlation b) negative correlation
c) no correlation d) a parallel correlation
Solution :
By observing the spread and drawing the line of best fit, we can draw the raising line. So, it will have a positive slope and it will have positive correlation.
Problem 2 :
Based on these results, if a team practice 4 hours per week next season, which is the best estimate of the number of debates the team can expect to win ?
a) 20 b) 12 c) 16 d) 1
Solution :
16 will be the best estimation.
Problem 3 :
Which of the following describes the correlation between gas that remained and the hours that he had passed ?
a) positive correlation b) negative correlation
c) no correlation d) undefined correlation
Solution :
While looking at the observation, we can draw the falling line as line of best fit. It will have negative slope and its slope will be negative. So, negative correlation.
Problem 4 :
The following data table and scatter plot represent the number of negative customer reviews for a given model of cell phone and the total number of that same cell phone model were sold.
Number of negative reviews 125 98 50 106 21 69 80 37 |
Number of cell phones sold(in thousands) 163 505 701 355 925 592 700 890 |
a) Points (37, 890) and (98, 505) are on the the line of best fit.
b) The scatter plot represents a negative correlation.
c) Its reasonable to predict that if there are 75 negative reviews the number of cell phones sold that same model will be close to 600,000.
Solution :
a) The points (37, 890) and (98, 505) are not on the line of best fit. It is false.
b) Yes, it is a negative correlation. True.
c) True.
Problem 5 :
A keyboard instructor at a community college collected data comparing a student's age and their typing speed. The equation for the line of best fit is given as
y = -1.4x + 117.8
where x is the age in years and y is the typing speed.
If you are 25 years of age, what is your typing speed ?
a) 153 words per minute b) 83 words per minute
c) 63 words per minute d) 102 words per minute
Solution :
y = -1.4x + 117.8
When x = 25
y = -1.4(25) + 117.8
y = -35 + 117.8
y = 82.8
83 words per minute. So, option b is correct.
Problem 6 :
Below is the number of clothes denoted to New York City homeless shelters in the given years.
a) Determine the equation of line of best fit using the given two points on the line of best fit, where x is the number years since 1992 and y is the number of clothes denoted in thousands.
b) Using the equation for the line of best fit predict the year in which only 38000 items of clothing will be denoted to the homeless shelters in New York City.
Solution :
y = mx + b
Slope (m) = (y_{2} - y_{1})/(x_{2} - x_{1})
(1996, 47) and (2012, 41)
= (41 - 47) / (2012 - 1996)
= -6/16
= -0.375
y-intercept (b) = 48.5
Equation of line of best fit :
y = -0.375x + 48.5
b) When y = 38000 (it is in thousands), so 38
38 = -0.375x + 48.5
38 - 48.5 = -0.375x
-10.5 = -0.375x
x = 10.5/0.375
x = 28
About 28 years.
Problem 7 :
At the Happy Paper Company the more boxes of paper you order the cheaper the price you have to pay of each box of paper. Below are the prices charged per box of paper to different companies ordering various quantities of paper.
Using the line of best fit, if your company wants to only pay $5.05 for each box of paper, how many boxes of paper should be ordered from Happy Paper Company ?
Solution :
About 3500 boxes.
Problem 8 :
A base ball coach graphs some data and finds the line of best fit. The equation for the line of best fit is
y = 0.32x - 20.51
where x is the number of times at bat and y is the number of hits.
How many hits should he expect from a player who is at bat 175 times ?
a) 35 hits b) 49 hits c) 609 hits
d) 62 hits
Solution :
y = 0.32x - 20.51
x = 175
y = 0.32(175) - 20.51
y = 56 - 20.51
y = 35.49
So, option a is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM