He medium prices of houses sold during the year ending june

Question

Complete the following questions using Microsoft Excel.

Exercise 1 - The Normal Distribution

The mean amount of pasta eaten by Italians each year is 26kg. If the amount follows a normal distribution with a standard deviation of 5 kg, in a random sample of 300 Italians, how many ( to the nearest whole number) would you expect to eat each year.

(a) Less than 30kg?

(b) More than 20kg?

(c) Between 20kg and 30kg?

Exercise 2 - Correlation

The medium prices of houses sold during the year ending June 2008 for 12 areas in Sydney, along with their postcodes, are shown in the following table

Suburb	Postcode (x)	Median price ($'000) (y)
Hazelbrook	2779	302
Penrith	2750	305
Greystanes	2145	404
Kellyville	2155	579
Croydon	2132	752
Cherrybrook	2126	890
Balmain	2041	993
Lane Cove	2066	1040
Birchgrove	2041	1115
Pymble	2073	1200
Queenscliff	2096	1375
Church Point	2105	1425

(a) Using a scale between 2000 and 2800 for postcode on the horizontal axis, and a scale between 300 and 1500 for median price ($'000) on the vertical axis, draw a scatter diagram of the data.

(b) For these data:

S_xx = 756 389     S_yy = 1 733 714    S_xy = -822 255

Calculate the value of the correlation coefficient.

(c) Test the value of found in (b) for significance. What conclusions can you draw?

Exercise 3 - Regression Analysis

The exchange rate between the Australian dollar (A$) and the US dollar (US$) on the 2^nd              of January is shown in the following table for each year between 2003 and 2012.  The data shows how many cents US that A$ would purchase.

Year	US Cents
2003	56.2
2004	75.0
2005	78.1
2006	73.3
2007	78.8
2008	87.5
2009	70.3
2010	89.7
2011	102.3
2012	97.9

(a) Plot the data on a scatter diagram and joint the points (place the year on horizontal axis) Do you see any linear trend? If not, What trend do you notice? Are there any outliers?

(b) Find the least squares regression line of US cents on year where the years are labelled as 1, 2, 3, 4, ..., 10.

(c) Draw the line found in (b) on the scatter diagram in (a). Do you think it's a good fit?