Question 1:

Suppose the value of investment properties is normally distributed witha mean of $550,000 and a standard deviation of $70,000. An investment property is randomly selected.

(a) What is the probability that the investment property selected is worth less than $400,000?

(b) What is the probability that the investment property selected is worth between $450,000 and $600,000?

(c) What is the value of a particular investment property if only 10% of all investment properties are more valuable than this property?

(d) One investor has 20 properties. What is the probability that the total value of these properties is more than $15 million?

Question 2: A random sample of 25 customers at the checkout in a small local supermarket revealed that they had spent the following amounts in the supermarket ($):

25 45505963538054 1218272930
65501572437160355549 15 54

(a) Give a point estimate for the mean amount per customer spent at the supermarket.

(b) Give a 99% confidence interval estimate for the mean amount per customer spent at the supermarket.

Question 3:

A leading company chemically treats its product before packaging.The company monitors the weight of product per hour that each machine treats. A simple random sample of 25 one hour periods from one machine was taken. The results in kilos are shown below:

165911708419172184511753618598172531462417589166251105816633197181921918421

17976179381680318830201092115115139199331821618523

(a) Can the company conclude that the mean kilo of product treated in one hour by this machine is more than 15,000? Use a 5% level of significance.

(b) What assumptions must be made for the test to be valid?