Question 1 - (1 mark each = 15 marks) Type The Letter Corresponding To Your Answers In Table Provided (anu answer not in the box provided will not be marked)

a) i

a) ii

a) iii

a) iv

a) If thefollowing are percentage changes in values of your total investment over the past nine years.

4, -2, 0, -5, 0, 2, 7, 8, 10

i. What is the sample mean?	A 3	B 2.67	C 2.5	D -2.6
ii. What is the median?	A 3	B 2.66	C 2	D 4
iii. What is the sample variance?	A 25	B 4.975	C 5	D 24.75
iv. What is the sample range?	A 6	B 10	C 2	D 15

b) i

b) ii

b) iii

b) iv

b) As input to pricing policy, the owner of a big store is interested in the relationship and details between the price and customrr's decision on whether to purchase extended warranty. Following are 300 sales invoices selected randomly with the event mentioned in the table below.

	Extended Warranty
	Purchased	Not Purchased	Total
Sale Price	30	70	100
Retail price	80	120	200
Total	110	190	300

One customer is selected at random. Let W be the event that the customer purchased the extended warranty, and let S be the event that the customer purchased at sale price.

i. What is P (W)?	A 0.13	B 0.66	C 0.33	D 0.37
ii. What is theP (W S)?	A 0.10	B 0.60	C 0.90	D 0.30
iii. What is theP (WU S)?	A 0.10	B 0.60	C 0.90	D 0.30
iv.What is the P (W | S)?	A 0.10	B 0.60	C 0.90	D 0.30

Question 1 cont. - Type The Letter Corresponding To Your Answers In Table Provided

c) i

c ii)

c) The records of a fancy shoe store show that 60% of customers making a purchase pay by credit card. Suppose 10 customers purchased shoes from the store yesterday morning.

i. What is the probability that at most three customers paid by credit card?

A 0.012 B 0.055 C 0.945 D 0.988

ii. What is the expected number of purchases made by credit card?

A 4 B 6 C 8 D 60

d) i

d ii)

d) The scheduling manager of an electricity supply company knows that the number of emergency calls follows a Poisson distribution with an average of 7 calls per week (7 days)

i. What is the probability that the company will receive exactly 2 emergency calls during a specified week?

A 0.030 B 0.970 C 0.023 D 0.993

ii. What is the probability that there will be at least four emergency calls on a given day?

A 0.173 B 0.918 C 0.996 D 0.019

e) i

e) ii

e) iii

e) Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50.

i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol?

A 2.5 B 0.0062 C 0.9938 D 0.0202

ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize?

A $56 B $184 C $3.50 D $217.60

iii. In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105?

A 0.0668 B 0.9332 C 0.3821 D 0.6179