An analyst predicted last year that the stock of Logistics, Inc., would offer a total return of at least 20% in the coming year. At the
beginning of the year, the firm had a stock market value of $6 million. At the end of the year, it had a market value o
Taylor and Mackurin Series
Taylor Series:
Informal way
f(x) = sum from n=0 to infinity of f^(n)(a)/n! * (x-a)^n
Mackuran:
f(x) = sum from n=0 to infinity of f^(n)(a)/n! * x^n
Partial Sum:
Tn(x) = sum from i=0 to n of f^(i)(a)/i! * (x-a)^i
(n-th de
Review
Theorem 1 Comparison Test
given cfw_an and cfw_bn positive sequences
If an <= bn for n>= K and sum bn converges then sum an converges
If an >= bn for n>=K and sum bn diverges then sum an diverges
Theorem 2 Limit Comparison Test
Given cfw_an and cfw
Review:
given cfw_an the series is devined as the sum from n=1 to infinity of an = a1 + a2 + an
Partial Sum:
sn = sum from i=1 to n of ai = a1 + a2 + an
Definition
if cfw_Sn converges then sum from n=1 to infinity of an converges
if cfw_Sn diverges
11.5 Alternating series
Definition
An alternating series is denoted by sum from =1 to infinity of (-1)^n * an = -a1 + a2 - a3 + a4 etc
Alternating Test
If an > 0 and an+1 <= an for n>= k
limit as n-> infinity of an = 0
then the sum of (-1)^n * an co
11.6 Absolute convergence, the ratio and root test
Definition: A series sum from n=1 to infiity of an is absolutely convergent (AC) if sum from n=1 to infinity of |an| converges
Definition: A series n=1 to infinity of an is called "conditional convergent"
Improper Integrals:
A comparison test:
Given f and g continuous with f(x) >= g(x) >= 0 for all x > a
If integral from a to infinity of f(x) dx converges then integral from a to infinity g(x) also converges
If integral from a to infinity of g(x) dx div
sum 4^(n-1)/3^n-2 = 4^(n_1)/3^n = (4/3)^n
Review: Gvien a secuqnces cfw_an
sum from n=1 to infinity of an = a1 + a2 + an
Partial Sum
Sn = sum from i=1 to n of ai = a1+a2+an
If cfw_Sn converges then
sum from n=1 to infinity of an = limit as n-> infi
11.1 Sequences
A sequence is a list of numbers
cfw_an] has limit L if an->L as n-> infinity
limit as n->infinity of an = L converges
Theorem 1
Given f IR -> IR such that
f(n)=an for all in IN
limit as x->infinity of f(x) = L
limit as n-> infinity of
Review THeorem (Integral Test) Given f continuous positive and decreasong for f(n) an
a. If integral from 1 to infinity of f(x) dx converges then the sum from n=1 to infinity of an converges
b. If the integral from 1 to infinity of f(x) dx diverges then
Review: Power Series
Definition: A power series is a series
sum from n=0 to infinity of Cn * x^n
Cn given constants, x variables
+ a series of form
sum from n=0 to infinity of Cn (x-a)^n
is called a "power series" in (x-a)
Theorem 1: Given a power se
Exercises 62
Seelii- 62 Applications ofioNormaJ Dim-teem 323
l. Admission ChargeiorMovies The average early-bird
special admission price for amovie is $5.8 LIfthe
distribution of nnvie adm'nsion charges isapproximately
rlJrrnal with astandard deviation
Homework # 6
MA111-Probability&Statistics
Due Date: Sunday, February 15, 2015
Please turn in solutions along with all work to each problem listed below.
Section 4.1: 10 , 12 , 14 , 15 , 16 , 20 , 24 , 29 , 40
MA 111- Homework 3 (#8) By Hand
A researcher wishes to determine if there is a relationship
between the number of days an employee missed a year and the
persons age. Draw a scatter plot and comment on the nature of
the relationship.
Age, x
Days missed, y
Homework 15
SEC. 8 2
P. 2
a. Ho; mean = 3262
H1; mean # 3262
b. . Critical Value = - / + 1.96 for confidence level a=0.05
Root square of 50 = 7.071
c. Test Value Z=(2995-3262) / 1100 /7.071 = - 267 /155.56= - 1.716
d. Dont reject Ho
e. Its significant evi
Quiz # 12
Question 1
2 out of 2 points
The Central Limit Theorem states that random samples chosen from a given population
will have averages that form a normal distribution if and only if the distribution from
which the samples were chosen formed a norma
Homework 15
SEC. 7 3
P. 4. Like 5 below
Book formula for estimation of p and Table of Z for 90 % Z1/2 value !
Z1/2 = 1.645
p between 0.388 and for 0.492 with 90 % confidence
P.5
p=55/450 =0.12
q=1-p=1-0.12=0.88
Z1/2 =1.96 for 95 % confidence
0.12 + / - 1.
Homework # 5
MA111-Probability&Statistics
Due Date: Sunday, February 8, 2015
Please turn in solutions along with all work to each problem listed below.
Use the TI83/84 to compute Descriptive Statistics:
The data below represents the length of time in year
Homework # 11
Due Date: Sunday, March 22, 2015
MA111 Probability & Statistics
Please show all work.
Section 6.2:
2 , 5 , 6 , 8 , 10 , 14 , 15
For each problem above, I want to see the probability that you are trying to find [ P( ) ],
the normalcdf( ) comm
MA 111- Discussion Board- Week 3
This weeks lesson involved the use of the TI83/84 graphing calculator. I would like you
to use this weeks discussion board to comment on a few ideas:
1.) How was your experience using the TI84/84? Did you have any prior ex
Quiz # 13
Question 1
2 out of 2 points
A 99% Confidence Interval is wider than a 95% Confidence Interval when
computed based on the same sample data.
Selected
Tru
Answer:
e
Correct
Tru
Answer:
e
Question 2
2 out of 2 points
If samples of size 15 are chose
Homework # 12
Due Date: Sunday, March 29, 2015
MA111 Probability & Statistics
Please show all work.
Section 6.2:
18 , 19 , 22 , 25 , 26 , 30
Note: Please use the distributions built into the TI83/84 to answer these
problems. Write the distribution used, t
Cards
Term
Definition
Statistics
Term
The science of conducting studies to collect,
organize, summarize, analyze, and draw
conclusions from data.
Definition
Variable
Term
A characteristic or attribute that can assume
different values (the final exam grade
Question 1
2 out of 2 points
A chi-square distribution is negatively skewed.
Selected
Answer:
Answers:
Fals
e
True
Fals
e
Question 2
2 out of 2 points
Sample proportions will always form a normal distribution.
Selected
Answer:
Answers:
Fals
e
True
Fals
e
Sample Midterm Exam
MA 111 - Probability & Statistics
Name:
Please show all work on this exam paper. Good Luck!
1.
The age of the signers of the Declaration of Independence are shown below.
41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 50 38
50 40 30 34
Week 11 Homework
SEC. 6 2
ALL probabilities from Table based on Z score
( computing Z - scores using formula in book or as shown in problems 14 +
15 bellow ! )
P. 2
P (35,000<X<45,000) =0.3031
P (X > 40,000) = 0.9131
P ( X< 31,000) = 0.0016
P. 5
P (200<X<
MA 111- Probability and Statistics
Homework # 12
Section 6.2: 18, 19, 22, 25, 26, 30
18. Middle Limit 50%
Lower limit (X1-mean)/ SD= z for 25%
Second upper (X2-means/SD= z for 75%
X btw. X1= 722.99 and X2 =861.01
19. Middle = 80%; 40% of the area ( probab