PC Ch4 and Ch6 Review
A group of teenagers is surveyed. The survey asks them how old they are (in years) and how many times
they have gone on a date (in dates). The data gathered is in the table below:
Age (years)
14
14.5
15
15.5
16
17
17.2
Number of dates (dates)
0
1
4
7
13
30
30
1) Which linear regression equation best models the above data?
A 𝑦̂ = 10.3𝑥 − 148.8
B 𝑦̂ = −148.8𝑥 + 10.3
C 𝑦̂ = 2.8𝑥 2 − 77.1𝑥 + 533
D 𝑦̂ = 160 ln 𝑥 − 426.8
2) What is the correlation coefficient of the linear regression equation from above.
A 𝑟 = 0.96
B 𝑟 = 0.97
C 𝑟 = 0.99
3) Extrapolate how many dates you would expect a 20 year old to have been on from the above
data.
A 54
4)
B 58
C 62
D 80
E 116
Which statement best reflects the relationship between age and number of dates?
A Higher age causes a higher number of dates.
B Higher age causes a lower number of dates.
C Higher age correlates well with a higher number of dates.
D Higher age does not correlate with number of dates.
E Higher age correlates well with a lower number of dates.
5) Which correlation coefficient is likely to be associated with the linear regression equation of the
above scatter plot?
A 𝑟 = −1
B 𝑟 = −0.7
C 𝑟=0
D 𝑟 = 0.7
E 𝑟=1
6) How many unique arrangements of the letters of the word ‘DELEVELED’ ?
A 96
7)
A 30
B 3780
C 2494800
D 39916800
Wytiaz Pizza Company has a menu that offers 15 pizza toppings. WPC does not handle requests
for multiple copies of the same topping. How many unique pizzas can be ordered with up to 2
toppings (you may assume that the 0 topping pizza called ‘plain’ is available)?
B 105
C 120
D 121
8) A math department made up of 8 teachers elects a department chair and a department vice
chair. How many ways can the leadership positions be selected?
A 16
B 28
C 56
D 40320
9) Mark visits store that sells fish and fish tank equipment. After browsing, Mark decides that he
wants to have a fish tank with 3 fish and a little castle for his fish to be able to swim through.
The store has 3 sizes of tank to choose from (large, medium, and small). The store has 50
different fish to choose from. The store has 7 different castles that could fit inside of a fish tank.
In how many unique ways can Mark buy his tank, fish, and castle?
A 1050
B 19610
C 411600
D 2469600
10) Expand the binomial: (𝑥 − 2)3
A 𝑥 3 + 6𝑥 2 + 12𝑥 + 8
B 𝑥 3 − 6𝑥 2 + 12𝑥 − 8
C 8𝑥 3 + 12𝑥 2 + 6𝑥 + 1
D 8𝑥 3 − 12𝑥 2 + 6𝑥 − 1
11) The 𝑎7 term of the binomial expansion of (𝑎 − 2)9 is given by which expression?
A (79)(𝑎)7 (2)2
B (79)(𝑎)2 (−2)7
C (79)(𝑎)2 (2)7
D (79)(𝑎)7 (−2)2
12) A cabinet used for storing sports equipment contains 10 soccer balls, 8 basket balls, and 7
footballs. All balls of each type are not distinguishable from one another. If a physical education
teacher selects 2 balls at random from the cabinet, what is the probability of not picking any
footballs?
A
4
15
B
51
100
C
3
50
D
49
100
13) Liz and Ben each put a quarter into a gumball dispenser that contains 4 red gum balls, 6 green
gum balls, and 5 blue gum balls. What is the probability that they each receive the same color of
gum ball?
A
1
2
B
60
7
C
7
60
D
31
105
14) The following data shows the total snowfall of each calendar year of Tigertown:
Year
2004
2005
2006
2007
2008
2009
2010
Inches of snowfall
73
84
73
80
16
105
73
What is the mean inches of snowfall?
What is the range of the inches of snowfall?
What is the mode of the inches of snowfall?
State the 5 number summary of the inches of snowfall:
Create a box and whiskers plot representing the inches of snowfall:
Are any of the amounts of snowfall outliers? If so, in which year did an outlier occur?
15) Tigertown has 1000 residents with a normally distributed IQ score. The mean IQ score is 112
with a standard deviation of 6. How many residents would you expect have an IQ score that is
between 100 and 124?
Reminder 1: The test has a free response portion. Revisit the more challenging problems from the HWs.
Reminder 2: Tests are cumulative. Expect material from previous chapters.