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.

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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

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