Suppose the value of investment properties is normally distributed with a mean o

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 $15 million?
Question 2 [13 marks]
A random sample of 25 customers at the checkout in a small local supermarket revealed that they had spent the following amounts in the supermarket ($):25455059635380541218272930655015724371603555491554(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 meanamount 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:16591170841917218451175361859817253146241758916625110581663319718192191842117976179381680318830201092115115139199331821618523(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?
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