Test for the fourth week
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 1 of 6
Assessment Activities sheet for Probability Sem XXXXXXXXXXPrint off and complete before handing in
Firstly fill in section A Name: XXXXXXXXXXGroup
Section A (4 marks)
Your student number is S
Your birthdate is
You will make some numbers using your student number
The first number, to be used in question 1, is the first two digits of your student number Now refe
ed as A
The second number will be used in Question 2. It is made from the last two digits in your student number
XXXXXXXXXXNow refe
ed as B
The Third number will be used Question 3, and is made using the third and fourth digits of your student
number
XXXXXXXXXXNow refe
ed as C
The seven numbers to be used in the fourth question will be made from the digits
1
First
Digit
1
Second
Digit
1
Third
Digit
1
Fourth
Digit
1
Fifth
Digit
1
Sixth
Digit
1
Seventh
Digit
List the 7 numbers you will be using in the box below, And this will be refe
ed to as data set D
Data set E will be made using your birthdate eg 30/12/95
1
First
Digit
1
Second
Digit
1
Third
Digit
1
Fourth
Digit
The year
digits added
List E here
If your student number was s XXXXXXXXXX
Then your seven numbers would be D
13 , 12 , 14 , 16 ,15 , 17 and 19
Eg. E Would become13,10, 11, 12 and(9+5=14)
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 2 of 6
Question 1 Complete the Venn Diagram ( 4 marks) and parts a) to h) (4 marks)
D E
D = {dataset D }
E = {dataset E }
Sample space = { 10 ≤Positive Integers ≤20 }
Find:
a) Pr(D)
) Pr (E)
c) Pr( D E)
d) Pr (D E)
e) Pr (D E) / D)
f) Pr(D’)
g) Pr(D E’)
h) Pr (D E)’
Do not enter repeats of any numbers, mention them just
once
In each set
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 3 of 6
Question 2 (4 marks)
There is a class of students in the statistics course at RMIT. When asked their favourite colour, there
were 3 distinct categories. The selected colour and gender of students are shown in this contingency
table. Make sure you fill in the values and the totals.
blue green red
male A B C
female B C A
If you were to approach a statistics student, what would be the probability that this student:
a) Was a female and has red as a favourite colour
) Was either a male who likes green or a female who likes blue
c) Was a male who likes blue given this person was a male
d) Was a female who likes green given this person likes green
XXXXXXXXXXmarks)
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 4 of 6
Question 3
The weight of a Dog is normally distributed with mean A kg and standard deviation 2.B. kg. (eg. If
your B is 45 then standard deviation is 2.B= 2.45)
Find:
a) The probability that a Dog is less than 35 kg ( 2 marks)
) b) The probability that a dog is greater than 32 kg ( 2 marks)
c) What dog’s weight would be at the start of the top 5% of the heaviest dogs. Interpret your
answer. ( 2 marks)
d) You sampled dogs 16 at a time and calculate the sample mean for the sample. What would the
sample mean be at the top ( heaviest) 10% of sample means sampled in this way? ( 2 marks)
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 5 of 6
Question XXXXXXXXXXmarks)
The amount of savings needed to fund a person’s retirement is a concern for the government. A
sample of C (if C happens to be 0, then use C as 25) people who were about to retire was taken. On
surveying this sample, it was found the average savings per person was $350,000 and the population
deviation is known to be $20,000. Calculate a 99% confidence interval for the population mean
amount needed for retirement
Question 5 (5 marks)
3) The proportion of people who love dogs is known to be quite high Australia wide. In an effort to
find the Population Proportion of people who love dogs, a sample of A was taken and 60% in this
sample said they did indeed love dogs. Construct a 95% confidence interval for the population
proportion of people who love dogs Australia wide. Be sure to interpret your answer XXXXXXXXXXmarks)
Assessment task Probability and probability Distributions XXXXXXXXXXdoc5
Semester 1
RMIT University Page 6 of 6
Question 6 (6 marks)
The likelihood that a person likes dogs is known to be 70%. A sample of (C + A) / 2 ( round off
to a whole number) is approached. Calculate
a) The probability that less than 2 will love dogs XXXXXXXXXXmarks)
) The probability that 6 will love dogs ( 2 marks)
c) The Expected (mean) number who will love dogs ( 1 mark)
No Slide Title
Business Statistics
Probability
Week 4, class 2: Contingency tables
Key concepts
Probability of single events
Contingency Tables
Probability of more than one event
Mutually exclusive events
Compliment of an event
Independent events
Resources, activities for this