4 Questions

1. A 90% condence interval for the mean income of shop assistants in a certain city
is found to be ($15,000, $18,000). Explain brie y what this means. Would a 95%
condence interval be better than a 90% one? Justify your answer.
(5 marks)
2. A charity believes that when it puts out an appeal for charitable donations the
donations it receives will be normally distributed with a mean of $50 and a standard
deviation of $6.
(a) Find the probability that the rst donation it receives will be less than $40.
(b) Find the value x such that 5% of donations are more than $x.
(5 marks)
3. A consultant for Dell was investigating computer usage among students at a
particular university. 200 undergraduates and 100 postgraduates were chosen at
random and asked if they owned a laptop. It was found that 81 of the
undergraduates and 63 of the postgraduates owned a laptop. The consultant
calculated that 48% (144 out of 300) of the students interviewed owned a laptop.
Explain, with reasons, whether the gure of 48% will be a good estimate of the
proportion of all students who own a laptop.
(5 marks)
4. For a certain variable, the standard deviation in a large population is equal to 12.5.
How big a sample is needed to be 99% sure that the sample mean is within 1.5 units
of the population mean?
(5 marks)