## BUSN1009 – Quantitative Methods

Assignment

(Due date: Monday, 27 August 2018, at 11.59pm midnight)

Note: Completed work must be typewritten and submitted on FLO. When submitting your work

(on FLO), write clearly your name and student ID.

Question 1. The number of customers that bought a cup of coffee from a street coffee shop in a

particular morning over a seven-day-period is as follows:

1 7 9 6 3 5 6

a. Find the mean, median and mode.

(1.5 marks)

b. Estimate the values of the 1st and 3rd quartiles and determine the interquartile range.

(1.5 marks)

c. Construct a box plot (note: make sure you indicate 5-number summary on the box plot).

(2 marks)

d. On the basis of your results above, comment on the shape of this distribution.

(2 marks)

Question 2. In a management trainee program 80% of trainees are female. 90% of the females

attended university, and 78% of males attended university.

a. Construct a tree diagram for this information (Note: Indicate conditional probabilities

and joint probabilities on the diagram). Using this information construct a joint

probability table.

(3 marks)

b. What is the probability that a trainee selected is a female university student?

(1 mark)

c. If a female trainee is selected what is the probability she is not a university student?

(1 mark)

d. Are gender and attending university independent? Explain.

(1 mark)

e. Are gender and attending university mutually exclusive? Can mutually exclusive events

be independent? Explain.

(2 marks)

2

Question 3. Consider two independent events, A and B, where the P(A) is 0.45 and the probability

that A does not occur or B occurs is 0.70. Determine the probability that event B occurs.

(2 marks)

Question 4. A recent study by the American Highway Patrolman’s Association revealed that 65%

of American drivers use their seatbelts. A sample of 12 drivers on major highways was

randomly selected.

a. Find the probability that seven of the drivers are wearing seatbelts.

(1 mark)

b. How many of the drivers would be expected to be wearing their seatbelt?

(1 mark)

c. Calculate the standard deviation for this distribution.

(1 mark)