4 Question

1. A 90% condence 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%

condence 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)