Suppose the value of investment properties is normally distributed with a mean of $550000 and a standard deviation of $70000. An investment property is randomly selected.(a) [5 marks]
What is the probability that the investment property selected is worth less than $400000? (b) [7 marks]
What is the probability that the investment property selected is worth between $450000 and $600000?(c) [7 marks]
What is the value of a particular investment property if only 10% of all investment properties are more valuable than this property?(d) [5 marks]
One investor has 20 properties. What is the probability that the total value of these properties is more than $15 million?
Question 2 [13 marks]
A random sample of 25 customers at the checkout in a small local supermarket revealed that they had spent the following amounts in the supermarket ($):25 45 50 59 63 53 80 54 12 18 27 29 30 65 50 15 72 43 71 60 35 55 49 15 54(a) [4 marks]
Give a point estimate for the mean amount per customer spent at the supermarket.(b) [9 marks]
Give a 99% confidence interval estimate for the mean amount per customer spent at the supermarket.
Question 3 [13 marks]
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:16591 17084 19172 18451 17536 18598 17253 14624 17589 16625 11058 16633 19718 19219 18421 17976 17938 16803 18830 20109 21151 15139 19933 18216 18523(a) [9 marks]
Can the company conclude that the mean kilo of product treated in one hour by this machine is more than 15000? Use a 5% level of significance.(b) [4 marks]
What assumptions must be made for the test to be valid?