Expert Answer:introduction to statistics

Answer & Explanation:Construct a frequency distribution for these data using a lower limit for the first class of 5 and a class width of 10. Indicate the class limits, boundaries, midpoints, frequencies and cumulative frequencies.
assignment1a_w.docx

assignment2a.docx

assignment3a.docx

Unformatted Attachment Preview

Assignment 1A
Total Marks = 70
Please show all your work. Some questions require you to use graphs, tree
diagrams, formulas, and so on that are difficult or impossible to reproduce
in word-processing programs, so you will have to print the entire
assignment and fill it out and mail it to your tutor. As an alternative to
mailing, you might be able to photograph or scan your assignment and
submit it through the appropriate drop box. If you do, make sure the
material you are submitting is legible.
Question 1
A random sample of 20 days showed the following number of cardiograms
done each day at an outpatient testing centre:
8 marks
45
25
39
5
42
48
35
12
40
16
36
27
37
30
18
22
32
54
44
29
Construct a frequency distribution for these data using a lower limit for the
first class of 5 and a class width of 10. Indicate the class limits, boundaries,
midpoints, frequencies and cumulative frequencies.
Note: As this data set does not contain fractional values, do not use the
“less than” method described on page 43 of the textbook for writing the
classes.
Introduction to Statistics
1
Question 2
The amount a mother spends on prenatal care can have a long-term impact
in terms of reducing complications resulting from a baby’s low birth weight.
A random sample of 50 new mothers was asked to estimate how much they
spent on prenatal care. The results are presented in the frequency
distribution below.
2
Amount Spent on
Prenatal Care ($)
Mothers
(Number)
0–99
100–199
200–299
300–399
400–499
2
4
8
20
16
Total
50
3 marks
a.
Calculate the mean amount spent on prenatal care.
5 marks
b. Use the short-cut formula to calculate the standard deviation of
amounts spent on prenatal care.
Mathematics 215 / Assignment 1A
4 marks
c.
Construct a relative frequency polygon of amounts spent on prenatal
care. Use ruler and the graph below to construct your answer.
Note: In addition to labeling the axes correctly, indicate the relative
frequency at each point on the polygon.
4 marks
d. Construct a percentage ogive of amount spent on prenatal care. Use
ruler and the graph below to construct your answer.
Note: In addition to labeling the axes correctly, indicate the cumulative
percentage at each point on the ogive.
Introduction to Statistics
3
4
2 marks
e.
Does the frequency polygon suggest skewness in the data? If so, in
which direction?
1 mark
f.
What percentage of mothers spent less than $200 on prenatal care?
Mathematics 215 / Assignment 1A
Question 3
Random samples of households were selected from each of three regions in
a large metropolitan area. The number of households selected from each
region and the corresponding mean household incomes are provided in the
table below.
4 marks
Region
Households Selected
(Number)
Mean Household Income
($1,000)
A
B
C
75
30
20
49
80
40
What is the mean household income for all three regions combined?
Question 4
4 marks
Introduction to Statistics
A course has two quizzes of equal weight, a midterm examination that has
twice the weight of a quiz, and a final examination that has twice the weight
of the midterm exam. If a student obtains 54% and 60% on the quizzes;
55% on the midterm; and 80% on the final, what will be the student’s
weighted mean final grade?
5
Question 5
5 marks
The mean amount spent by all customers at an organic food market is
estimated to be $48, and the standard deviation is estimated to be $12.
According to Chebyshev’s Theorem, at least what percentage of customers
would be expected to spend between $27 and $69?
Note: Express your answer to two decimal places of accuracy.
6
Mathematics 215 / Assignment 1A
Question 6
The following data represent ozone readings, in parts per million (ppm),
taken at 3:00 p.m. for a random sample of 18 days.
12
34
8
15
11
18
10
21
12
13
14
17
4
8
20
9
40
21
4 marks
a.
2 marks
b. In what direction, if any, are the data skewed?
2 marks
c.
5 marks
d. Calculate the standard deviation of ozone readings. Use the short-cut
formula.
Introduction to Statistics
Construct a stem-and-leaf display for these data. Place the leaves in
ascending order.
Calculate the mean ozone reading.
7
8
5 marks
e.
Calculate the quartiles and the interquartile range.
5 marks
f.
Sketch a box-and-whisker plot on the graph below. Indicate any
outliers.
1 mark
g.
Within what range do the middle 50% of ozone readings fall?
Mathematics 215 / Assignment 1A
3 marks
h. Calculate the approximate value of the 70th percentile. What does this
number tell you?
3 marks
i.
Introduction to Statistics
What is the percentile rank of an ozone reading of 15? What does this
number tell you?
9
Assignment 2A
Total Marks = 65
Please show all your work. Some questions require you to use graphs, tree
diagrams, formulas, and so on that are difficult or impossible to reproduce
in word-processing programs, so you will have to print the entire
assignment and fill it out and mail it to your tutor. As an alternative to
mailing, you might be able to photograph or scan your assignment and
submit it through the appropriate drop box. If you do, make sure the
material you are submitting is legible.
Question 1
A class of 50 students obtained the following grades in a statistics course:
A
5
B
25
C
15
D
5
If one student is selected at random, what is the probability that
1 mark
a.
2 marks
b. the student obtained either a B or a C?
2 marks
c.
2 marks
d. the student did not obtain either a B or a C?
Introduction to Statistics
the student obtained a B?
the student did not obtain a D?
1
Question 2
A realty company has 100 homes listed for sale. Some of these homes have
fireplaces, some have garages, and some have neither. A breakdown is
provided in the two-way classification table below.
Garage (G)
No Garage (G)
a.
2
Fireplace
(F )
No Fireplace
(F )
50
10
30
10
If one of these 100 homes is selected at random,
1 mark
i.
what is the probability that the home selected does not have a
fireplace?
3 marks
ii. what is the probability that the home selected has a fireplace or a
garage?
2 marks
iii. what is the probability that the home selected has neither a
fireplace nor a garage?
2 marks
iv. what is the probability that the home selected has a garage but not
a fireplace?
2 marks
v.
what is the probability that the home selected has a garage, given
that it has a fireplace?
Mathematics 215 / Assignment 2A
4 marks
b. Are the events F = Fireplace and G = Garage independent? Show your
proof.
2 marks
c.
Introduction to Statistics
Are the events F and G mutually exclusive? Why?
3
Question 3
An person has applied for positions at Company A, Company B, and
Company C. The probability of obtaining an offer from Company A is 0.4,
from Company B is 0.3, and from Company C is 0.6. Assume that the three
job offers will be independent.
2 marks
a.
What is the probability that the person will receive job offers from all
three companies?
2 marks
b. What is the probability that the person will receive a job offer from
Company B only?
2 marks
c.
4 marks
d. What is the probability that the person will receive exactly one job offer
from the three companies?
What is the probability that the person will receive a job offer from at
least one of the three companies?
Hint: Construct a tree diagram.
4
Mathematics 215 / Assignment 2A
Question 4
A city council consists of 7 males and 4 females. Two councilors are selected
at random to represent the city at an Elton John concert. What is the
probability that
2 marks
a.
both councilors are male?
5 marks
b. one councilor is a male and one a female?
2 marks
c.
at least one councilor is a female?
Note: Express probabilities to 4 decimal places of accuracy.
Hint: Construct a tree diagram.
Introduction to Statistics
5
Question 5
A machine used in a production process is set up correctly 97% of the time.
Given that the machine is set up correctly, only 5% of the items it produces
are defective, while 95% are not defective. On the other hand, if the
machine is set up incorrectly, 60% of the items it produces are defective,
while only 40% are not defective.
5 marks
What is the probability that a randomly selected item from the production
process will not be defective?
Note: Express probabilities to 4 decimal places of accuracy.
Hint: Construct a tree diagram.
6
Mathematics 215 / Assignment 2A
Question 6
5 marks
Introduction to Statistics
In a survey of 100 business executives, 60 per cent were male and 40 per
cent were female. Seventy per cent of the male executives used a PDA
(personal digital assistant). Overall, 60 per cent of the executives used a
PDA. Construct a two-way classification table for the survey results.
7
Question 7
You are given the probabilities listed below.
P ( A ) = 0.25
P ( B ) = 0.30
P ( C ) = 0.55
P ( A and C ) = 0.05
P ( B and C ) = 0
P ( B | A ) = 0.48
8
2 marks
a.
Are A and B independent events? Why or why not?
2 marks
b. Find P(A and B).
2 marks
c.
2 marks
d. Find P(A|B).
2 marks
e.
Are B and C mutually exclusive events? Why or why not?
3 marks
f.
Are B and C independent events? Provide a mathematical proof.
Find P(A or B).
Mathematics 215 / Assignment 2A
Assignment 3A
Total Marks = 70
Please show all your work. Some questions require you to use graphs, tree
diagrams, formulas, and so on that are difficult or impossible to reproduce
in word-processing programs, so you will have to print the entire
assignment and fill it out and mail it to your tutor. As an alternative to
mailing, you might be able to photograph or scan your assignment and
submit it through the appropriate drop box. If you do, make sure the
material you are submitting is legible.
Question 1
Let the random variable x represent the number of automobiles that a top
salesperson will sell to a corporate client. The only possible values for x are
0, 1 and 2, and the probabilities for each of these values may be calculated
from the formula
x
P ( x ) = 0.5 − ( ) where x = 0, 1 or 2
6
4 marks
a.
Construct the probability distribution of the variable x .
Note: Express your probabilities to 4 decimal places of accuracy.
2 marks
b. Calculate the mean of this probability distribution.
4 marks
c.
Introduction to Statistics
Calculate the standard deviation of this probability distribution.
1
d. What is the probability that a randomly selected top salesperson will
sell
2
2 marks
i.
at least 1 automobile to a corporate client?
2 marks
ii. at most 1 automobile to a corporate client?
1 mark
iii. exactly 1 automobile to a corporate client?
Mathematics 215 / Assignment 3A
Question 2
According to a recent study, 38% of all women will suffer a hip fracture
because of osteoporosis by the age of 85. If six women aged 85 are
randomly selected, what is the probability that
3 marks
a.
6 marks
b. At least four of them will suffer (or have suffered) a hip fracture due to
osteoporosis?
4 marks
c.
Introduction to Statistics
None of them will suffer (or has suffered) a hip fracture due to
osteoporosis?
Fewer than two of them will suffer (or have suffered) a hip fracture due
to osteoporosis?
3
Question 3
Seventy per cent of the student body of a very large post-secondary
institution is female. In a random sample of 12 students, what is the
probability that
4
3 marks
a.
at most half will be females?
3 marks
b. more than 7 will be females?
3 marks
c.
fewer than 3 will be males?
Mathematics 215 / Assignment 3A
Question 4
Use the standard normal distribution table to find
2 marks
a.
P( z  2.00) .
2 marks
b.
P(O  z  1.75) .
Introduction to Statistics
5
Question 5
Test scores on a university admissions test are normally distributed, with a
mean of 500 and a standard deviation of 100.
6
4 marks
a.
What is the probability that a randomly selected applicant scores
between 425 and 575?
4 marks
b. What is the probability that a randomly selected applicant scores 625 or
more?
Mathematics 215 / Assignment 3A
2 marks
c.
What is the probability that a randomly selected applicant scores less
than 500?
4 marks
d. Twenty per cent of test scores exceed what value?
Question 6
4 marks
The life span of a DVD player produced by one major company is known to
be normally distributed with a mean of 6.2 years. If 4.01% of these DVD
players have a life span of more than 8 years, what is the standard deviation
of the DVD player’s life span?
Introduction to Statistics
7
Question 7
It is estimated that, in jury trials, the jury will reach the correct decision
(guilty or not guilty) 92% of the time. In 200 randomly selected jury trials,
8
4 marks
a.
what is the probability that the jury will reach the correct decision in at
least 175 of the trials?
3 marks
b. what is the probability that there will be fewer than 180 correct
decisions?
4 marks
c.
What is the probability that there will be exactly 184 correct decisions?
Mathematics 215 / Assignment 3A
…
Purchase answer to see full
attachment