Download PROBABILITY AND STATISTICS SUMMER PACKET STUDENT

PROBABILITY AND STATISTICS SUMMER PACKET
STUDENT NAME :………………………….
Due Date: Sept 9,2013
This packet is your FIRST GRADE FOR MARKING PERIOD 1
Student signature:……………………………………
Current Grade : ……………..
Date Received :……………..
Parent signature: …………….
Date Received : …………….
Prob Stat summer packet 2013
Page 1
Topic: Summation Notation
5
Example 1:
å3k
4
Example 2:
k=1
åk
2
k=1
Solution
Solution
3(1) + 3(2) + 3(3) +3(4) + 3(5)=
12 + 22 + 32 + 42 =
3 + 6 + 9 + 12 + 15 = 45
1 + 4 + 9 + 16 = 30
Practice Problems
Directions: Evaluate each expression.
11
A.
 ( 2k  7)
k 1
9
B.
 (8k
2
 3k )
Answer: ______________
2
 2k  8)
Answer: ______________
k 1
10
C.
 ( 4k
Answer: ______________
k 1
Prob Stat summer packet 2013
Page 2
100
D.
åk
Answer: ______________
k=1
Topic: Slope of a Line (given two points)
Slope Formula: m =
y2 - y1
x2 - x1
Example 1: Find the slope of the
line that passes through (1,2) and
(3,4)=
Example 2: Find the slope of the
line that passes through (1,6) and
(3,8)=
Solution
Solution
Practice Problems
Directions: For the problems below, find the slope of the line between each
of the two given points. Write your answer in simplest form.
A. (1, 5) and (7, 8)
Answer: ______________
B. (-5, 9) and (5, 11)
Answer: ______________
C. (12, 13) and (7, 13)
Answer: ______________
Prob Stat summer packet 2013
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D. (-8, 2) and (-8, 7)
Answer: ______________
Topic: Permutations
n!
Permutation Formula: Notation - nPr =
( n - r )!
Example 1: Evaluate 3 P 7
Solution
7!
=
(7 – 3)!
7! = 7x6x5x4x3x2x1
4!
4x3x2x1
7 x 6 x 5 = 210
Example 2: How many
different ways can first,
second, and third place be
awarded to 10 people?
Solution
n = 10 people
r = 3 (1st , 2nd , 3rd place)
10! = 10!
(10 – 3)!
7!
= 10x9x8x7x6..
7x6…
10x9x8 = 720
Directions: Evaluate the following expressions
A. 12 P 3
Answer: _______________
B. 8 P 5
Answer: _______________
C. In how many ways can a president, a treasurer and a
secretary be chosen from among 7 candidates?
Prob Stat summer packet 2013
Page 4
Answer: _______________
D. How many ways can 1st, 2nd, 3rd, and 4th place be awarded to
10 runners?
Answer: _______________
Topic: Combinations
n!
Combination Formula: Notation – nCr =
( n - r )!r!
Example 1: Evaluate 3 C 7
Solution
7!
=
(7 – 3)!3!
4x3x2x1
7! =
4!3!
7x6x5x4!
4!x3x2x1
7 x 6 x 5 = 210 = 35
3x2x1
6
Example 2: Five cousins at a family
reunion decide that three of them
will go to pick up a pizza. How
many ways can they choose three
people to go?
Solution
n=5
r=3
5! =
5! = 5 x 4 x 3!
(5 – 3)!3! 2! 3!
2 x 1 x 3!
5 x 4 = 20
2x1
2
Directions: Evaluate the following expressions
A. 12 C 3
Answer: _______________
B. 8 C 5
Answer: _______________
C. In how many ways can a president, a treasurer and a
secretary be chosen from among 7 candidates?
Prob Stat summer packet 2013
Page 5
Answer: _______________
D. Problem: From a group of 40 people, a jury of 12 people is
selected. In how many different ways can a jury of 12 people
be selected?
Answer: _______________
Topic: Venn Diagrams
Example 1: Out of forty students, 14
are taking English Composition and
29 are taking Chemistry. If five
students are in both classes, how
many students are in neither class?
Example 2: Out of forty students, 14
are taking English Composition and
29 are taking Chemistry. If five
students are in both classes, how are
in either class?
Solution
Solution
Two students are taking neither
class.
There are 38 students in at least
one of the classes.
Directions: Create a Venn diagram to display the information then solve.
A. In a class of 87 students, 40 take Chorus, 53 take Band, and 16 take
both Chorus and Band. How many students in the class are not
enrolled in either Chorus or Band?
Prob Stat summer packet 2013
Page 6
B. In a school of 800 students, 185 students are taking Spanish, 160
students are on sports teams, and 72 students participate in both
activities. How many students don’t participate in either activity?
C. A veterinarian surveys 46 of his patrons. He discovers that 17 have
hamsters, 21 have guinea pigs, and 19 have birds. Eight have
hamsters and guinea pigs, and 5 people have a guinea pig and a bird.
Seven have hamsters and a bird, and of these, 3 people have a guinea
pig. How many patrons have none of these pets?
Topic: Writing equations of lines (using slope & y-intercept)
Slope Intercept Form: y = mx + b
Example 1: Find the slope of the line Example 2: Find the slope of the line
that passes through (1,2) and has a
that passes through (1,6) and (3,8) =
slope of 5.
Solution
Solution
8-6 2
Find the slope first:
= = 2
3 -1 1
Plug in the slope (m) and point (x,y),
then solve for b:
Use the m = 2 and any point and plug
2 = 5(1) + b
it in to the slope-int formula to solve
2=5+b
for b:
-3 = b
6 = 1(2) + b
Now take m = 5 & b = -3 and write
your equation in slope-int form:
y = 5x – 3
6=2+b
4=b
Now take m = 2 & b = 4 and write
your equation in slope-int form:
y = 2x + 4
Directions: Write the equation of the line using the given information.
A. Passes through (2,4); slope of 3
Prob Stat summer packet 2013
Answer: _______________
Page 7
1
5
Answer: _______________
C. Passes through (0, 0); m = -4
Answer: _______________
D. Passes through (5, 1) & (3, 0)
Answer: _______________
B. Passes through (-5, 8); m =
E. Passes though (-2, 3) & (-2, -1)
Topic: Standard Deviation
Standard Deviation Formula:
s=
Answer: _______________
å( x - m)
2
N
Example: What is the population standard deviation for the numbers: 75, 83, 96,
100, 121 and 125?
Solution
Firstly find the mean:
Mean = (75 + 83 + 96 + 100 + 121 + 125) ÷ 6 = 600 ÷ 6
= 100
Next find the variance. To calculate the Variance, take each difference, square
it, and then average the result:
(75 - 100)2 + (83 - 100)2 + (96 - 100)2 +
(100 - 100)2 + (121 - 100)2 + (125 - 100)2
= (-25)2 + (-17)2 + (-4)2 + (0)2
+ (21)2 + (25)2 = 625 + 289 + 16 + 0 + 441 + 625
= 1,996 So the Variance = 1,996 ÷ 6 = 332.66...
The Standard Deviation is just the square root of the Variance = √(332.66...)
Prob Stat summer packet 2013
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= 18.2 correct to 1 decimal places
Directions: Calculate the standard deviation for each problem
A. Ten friends scored the following marks in their end-of-year
math exam:
23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%,
72% and 82%
Answer: ______________
B. A booklet has 12 pages with the following numbers of
words:
271, 354, 296, 301, 333, 326, 285, 298, 327, 316,
287 and 314
Answer: ______________
Topic: Stem and Leaf Plots
Prob Stat summer packet 2013
Page 9
Example: "32" is split into "3" (stem) and "2" (leaf).
Directions: Find the mean, median, mode, and range for each.
A. Mean: _____________
B. Mean: _____________
Median: _____________
Median: ____________
Mode: _______________
Mode: _______________
Range: _______________
Range: ______________
Prob Stat summer packet 2013
Page 10
Topics: Frequency Tables
A Frequency Histogram is a special histogram that uses vertical columns to
show frequencies (how many times each score occurs):
Here I have added up how often 1 occurs (2 times),
how often 2 occurs (5 times), etc, and shown them as a
histogram.
Directions: Find the mean, median, mode, range, and the quartiles.
Prob Stat summer packet 2013
Page 11
Mean = __________
Median = _________
Mode = ___________
Range = ___________
Q1 = ______________
Q2 =_____________
Q3 = _____________
Topics: Box-and-Whisker Plots (Quartiles)
Example: 5, 8, 4, 4, 6, 3, 8
Put them in order: 3, 4, 4, 5, 6, 8, 8
Cut the list into quarters:
And the result is:
• Quartile 1 (Q1) = 4
• Quartile 2 (Q2), which is also the Median, = 5
Quartile 3 (Q3) = 8
Directions: Find the quartiles (Q1, Q2, Q3) for each example:
A. 8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6
Prob Stat summer packet 2013
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B. 13, 18, 6, 20, 25, 11, 9, 18, 3, 30, 16, 9, 8, 23, 26, 17
C. 4, 5, 6, 8, 9, 11, 13, 16, 16, 18, 20, 21, 25, 30, 31, 33, 36, 37, 40, 41
D.
Probability & Statistics
Summer Packet
Student Name: _________________________
Summer Resource Contact:
Due Date: 9/10/2013
[email protected]
[email protected]
This packet is the FIRST TEST GRADE of Marking Period 1
Student Responsibilities
I will be able to improve my math performance by:
 Completing the summer math packet
Prob Stat summer packet 2013
Page 13
 Reviewing math skills throughout the summer
____________________________ _________________
Student Signature
Current Grade
_______________
Date Received
Parent Responsibilities
Parents will be able to ensure student success in math by
 Supporting the math goal of ACHS
 Monitoring student completion of the summer packet
____________________________ _________________
Parent Signature
Date Received
Prob Stat summer packet 2013
_________________
Date Reviewed
Page 14