a) A researcher conducted a monthly survey on consumer confidence using face-to-face interviews. A survey conducted in 2005 found that 34% of Australians thought they were better off than in 2004. 55% of those surveyed said it was a good time to buy major household items. Suppose that of those who said they were better off than last year, 81% said it was a good time to buy household items. An Australian is selected randomly.

(i) What is the probability that this person thinks that they are better off than last year and it is a good time to buy household items?

(ii) What is the probability that this person thinks that they are better off than last year or it is a good time to buy household items?

(iii) What is the probability that this person thinks that neither are they better off than last year nor is it a good time to buy household items?

b) A survey of holiday accommodation in New Zealand showed that the occupancy

rate for all holiday accommodation in Wellington, excluding caravan parks and

camping grounds, was 40%. A random sample of 20 holiday accommodation

facilities is selected in Wellington. What is the probability that less than a quarter

of them are full?

c) Assuming the value of investment properties is normally distributed with a mean

of $230,000 and a standard deviation of $75,000. An investment property is

randomly selected. Find the probability that the property is worth less than

$250,000.