STAM4000 QUANTITATIVE METHODS
Assignment 2 – 2013 Trimester 1
To be submitted Friday 7thJune (Week 11) by 5pm at the front desk (*This extension was granted due to public holidays- please see the course outline)
General guidelines for submission
This is an individual assignment.
Answer all questions, clearly show your workings and include relevant graphs or statistical output to support your answers.
The assignment should be produced in Microsoft Word and a printed copy needs to be submitted by the due date.
You may use Microsoft Excel or any other statistical software.Pleasecopy and paste any relevant output into the Microsoft word document.
This assignment is worth 20% of the available course marks.
Question 1 (18 marks)
An entire population of English speaking adults living on a remote island named Statistica underwent IQ testing and the recorded IQ scores are presented in the file QMAssignment 2.xls.
Examine the data and determine if the distribution of IQ scores could be normal. You should confirm or reject normality by means of a visual inspection of the shape of the distribution. [2 marks]
Assume now that the distribution of IQ scores in Statistica is indeed normal with parameters equal to the mean and standard deviation of the given population data.
What proportion of the population falls into the “gifted” category where gifted is defined as an IQ score in the range 130 to 144? [3 marks]
What proportion of the population falls into the “genius” category where genius is defined as an IQ score above 144? [2 marks]
An alternative definition of “genius” is someone with an IQ score above the 99.9th percentile score. Under this definition, what is the minimum IQ score to be classified as a genius? [3 marks]
Suppose that a random sample of 150 Statistica residents is selected.
What is the probability that the average IQ of this sample is below 95?
Use Excel or other software to obtain an exact probability value.[3 marks]
What is the probability…