ASSIGNMENT NAME: ASSIGNMENT 2 – Probability COURSE: BSTA300 WEEK NUMBER: 7 CONTACT: Instructor via Blackboard Mail DUE DATE: See Critical Path document A. INSTUCTIONS Using Word, please answ

ASSIGNMENT NAME: ASSIGNMENT 2 – Probability

COURSE: BSTA300

WEEK NUMBER: 7

CONTACT: Instructor via Blackboard Mail

DUE DATE: See Critical Path document

A. INSTUCTIONS

Using Word, please answer the questions below. When answering the questions be sure to show your work. A formula sheet has been attached to help with some of the special characters and formula in your answers.

BE SURE TO STATE QUESTION NUMBER AND LETTER. (e.g. Question 1 b)

At the bottom of this page you will find two attached files:

A formula sheet, Formula .doc, that has two purposes:

To give you any formula you may need.

To allow you copy formula and special characters from the Word document into your Word answer sheet.

A template sheet, template2.doc, that you can use to answer the questions.

Download the attached files:

Click Formula .doc in the Attachments: section below.

Click Save for Internet Explorer. Firefox will open the file in Word.

Save the file in a folder you have set aside for class work (e.g. “BSTA300”).

Repeat steps i – iii to download template2.doc.

B. QUESTIONS

Question 1: (7 marks)

Olympia Sports store wants to determine whether or not to concentrate its advertising on athletic shoes for the “serious” athlete or the “weekend” athlete. The store also wants to know which type of use is the most popular. The marketing department gathered the following information from randomly selected customers.

Athlete Tennis Running Basketball

Serious 36 27 52

Weekend 54 66 30

Find the probability that if one customer is randomly selected he/she is a serious athlete and buys a shoe primarily for running.

Find the probability that if one customer is randomly chosen he/she is a serious athlete or an athlete who buys shoes for tennis.

Given that a customer buys shoes for basketball, find the probability that the customer is a weekend athlete.

If two customers are randomly chosen (without replacement), find the probability that they will both buy shoes primarily for tennis.

Question 2: (7 marks)

A couple plans to have 4 children.

List the different outcomes according to the gender of each child. Assume that these outcomes are equally likely.

How many events are possible?

Find the probability of getting exactly 2 girls.

Find the probability of getting exactly 2 children of each gender.

Question 3: (4 marks)

In a casino game craps, you can bet the next roll of the two dice with result in a total of 2. The probability of rolling 2 is 1/36. Find the odds against rolling 2.

If you bet $5 that the next roll of the dice will be 2, you will collect $155 (including your $5 bet) if you win. First identify the net profit, then find the payoff odds.

Question 4: (2 marks)

A supervisor must visit 8 different distribution locations around the country. She can visit them in any order, but wishes to find the most convenient sequence. How many sequences are possible?

Question 5: (4 marks)

There are 12 members on the board of directors for Cliffside General Hospital.

If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?

If they must form an ethics subcommittee of 4 members, how many different subcommittee are possible?

Question 6: (6 marks)

In a market study for Zellers, a researcher found that 70% of customers are repeat customers. If 12 customers are selected at random, find the probability of getting.

Exactly 9 of them are repeat customers

At least 9 of them are repeat customers

At most 9 of them are repeat customers

Attachment 1

Attachment 2

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BSTA 300

FORMULA SHEET

Terminolgy

Population: complete collection of all elements to be studied

Sample: sub collection of elements drawn form a population.

Parameter: a numerical measurement of a population characteristic.

Statistic: a numerical measurement of a sample characteristic.

Nature of data

Qualitative data, Quantitative data (continuous or discrete)

Levels of measurement: Nominal level, ordinal level, interval level, ratio level

Sampling: random, stratified, cluster, systematic, convenience

Organization of data

Frequency table, relative frequency, cumulative frequency

Relative frequency =

s

frequencie

of

sum

frequency

class

Class width = round up of

ervals

of

range

int

#

,

# of intervals =

width

class

range

Measures of centre (Measures of central tendency)

Population data

Sample data

Arithmetic mean

µ=

N

X

∑

n

x

x

∑

=

Position of median

2

1

+

N

2

1

+

n

Mode

Most frequent observation

Mid range

2

lowest

highest

+

Weighted mean

∑

∑

w

x

w

)

.

(

where w =weighting factor

x = individual value

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Measures of variation (dispersion)

Population data

Sample data

Range

Highest value – lowest value

Mean absolute deviation

N

X

∑

–

μ

n

x

x

∑

–

Standard deviation

σ =

N

X

∑

–

2

)

(

μ

s =

(

29

1

2

–

–

∑

n

x

x

s =

)

1

(

)

(

)

(

2

2

–

–

∑

∑

n

n

x

x

n

Variance

2

σ

s

2

Coefficient of variation (CV)

CV =

μ

σ

.100%

CV =

x

s

.100%

Measures of position: Deciles, quartiles, percentiles

Percentile of value (x)

=

values

of

number

total

x

than

less

values

of

number

Value of specific percentile (P

k

)

L =

n

k

)

100

(

where n = number of values in the data set

k = designated percentile

L = position of designated percentile in data set

If L is a whole number the value of k

th

percentile is found midway between the L

th

value and the next higher value in the original data set.

If L is a decimal, round L up to the next larger whole number, the value of P

k

is

counting from the lowest.

Coefficient of correlation (r)

∑

∑

∑

∑

∑

∑

∑

–

–

–

=

2

2

2

2

)

(

)

(

)

(

)

(

)

(

)

(

y

y

n

x

x

n

y

x

xy

n

r

Coefficient of determination (r

2

):

iation

total

iation

lained

r

var

var

exp

2

=

Regression equation

)

(

ˆ

1

0

x

b

b

y

+

=

,

(or

bx

a

y

+

=

ˆ

)

Where

∑

∑

∑

∑

∑

–

–

=

2

2

1

)

(

)

(

)

)(

(

)

(

x

x

n

y

x

xy

n

b

,

and

n

x

b

n

y

b

∑

–

∑

=

1

0

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ASSIGNMENT # 2

NAME:

Question 1

a.

b.

c.

d.

Question 2

a.

b.

c.

d.

Question 3

a.

b.

Assignment #2

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Question 4

Question 5

a.

b.

Question 6

a.

b.

c.

Assignment #2

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