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Question 1    4 Marks
The following data shows the amount of money (in dollars) spent by a sample of 24 customers at the local fast food restaurant.
23    14    32    9    32    14    25    8    4    19    21    11
17    18    19    42    26    21    17    19    21    6    9    18
(a)    Construct a stem-and-leaf diagram using this data.     1 mark
(b)    The restaurant believes that the average spending of customers is usually less than $25. Using your answer in (a), comment on this statement (Use 20 to 30 words).    1 mark
(c)    Recommend and draw the most suitable graph for this data. (Use 30 to 50 words to answer this part)    2 marks

Question 2    4 Marks
The following data shows the share prices (in dollars) of BMW in the month of November 2015.
Date    Prices ($)
23 Nov 2015    98.45
20 Nov 2015    99.17
19 Nov 2015    98.73
18 Nov 2015    97.45
17 Nov 2015    97.26
16 Nov 2015    94.71
13 Nov 2015    94.54
12 Nov 2015    94.46
11 Nov 2015    96.18
10 Nov 2015    95.93
9 Nov 2015    94.96
6 Nov 2015    96.03
5 Nov 2015    92.78
4 Nov 2015    92.45
3 Nov 2015    93.57
(a)    Calculate the mean and standard deviation for this data.    2 marks
(b)    Calculate the Minimum, Q1, Median, Q3 and Maximum values for this data.    2 marks

Question 3    4 Marks
The table below is taken from the Australian Bureau of Statistics website. It provides data on household use of the Internet from 2006 to 2013 in Australia.
        Households with Internet access
    Year
Frequency        2006–07    2007–08    2008–09    2010–11    2012–13
        '000    '000    '000    '000    '000
    Every day    3,321    3,703    4,281    5,157    5,933
    At least weekly    1,561    1,540    1,382    1,339    1,202
    At least monthly    185    176    132    148    129
    At least yearly    21    26    25    20    23
    Never    31    25    33    39    31
    Don't know    19    20    26    21    26
    Total    5,138    5,492    5,878    6,724    7,343
(a)    Find the probability that a randomly selected households access the Internet in 2010-2011.    1 mark
(b)    In the years of 2006-2007, what is the probability that a randomly selected households use the Internet every day?    1 mark
(c)    What is the probability that a randomly selected households access the Internet at least monthly or at least yearly?    1 mark
(d)    What is the probability that a randomly selected households access the Internet at least on monthly basis in 2007-2008?    1 mark

Question 4    4 Marks
(a)    Fiberglass manufacturing company finds 10% defective items in their production output. The production manager has been instructed to analyse and recommend solutions for improving the process. If a sample of 20 items is inspected, what is the probability of finding exactly two or three defectives?    1 mark
(b)    An emergency unit at the local hospital has admitted an average of 20 patients per hour. What is the probability that the next patient will be admitted at least 5 minutes from now?    1 mark
(c)    It is observed that the average share prices of ANZ Bank are normally distributed with a mean of $27 and a standard deviation of $2.
(i) What proportion of the share prices is between $25 and $35?



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