### Question 1

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.

**b.**The restaurant believes that the average spending of customers is usually less than $25. Using your answer in (a), comment on this statement .

**c.**Recommend and draw the most suitable graph for this data.

### Question 2

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.

**b.**Calculate the Minimum, Q1, Median, Q3 and Maximum values for this data.

### Question 3

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.

**b.**In the years of 2006-2007, what is the probability that a randomly selected households use the Internet every day?

**c.**What is the probability that a randomly selected households access the Internet at least monthly or at least yearly?

**d.**What is the probability that a randomly selected households access the Internet at least on monthly basis in 2007-2008?

### Question 4

**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?

**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?

**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?

(ii) What value do the upper 5% of the share prices exceed?

### Question 5

**a.**An operator for a telephone-answering service answers a large number of calls for two real estate agents. The two agents are charged the same monthly fee for this service and it is assumed that they will each receive approximately half the calls coming in. Based on this assumption, find the probability that in the next 150 calls 90 or more will be for one agent. (Use normal approximation of the binomial distribution.)

**b.**A recent survey conducted by a Fitness Society found that 60% of Australians who exercise daily by walking are women. If a random sample is taken of 15 people who exercise daily, what is the approximate probability that there will be an exactly 11 females in the group?

**c.**A study on online shopping habits found that men spend a mean of $2,401, whereas women spend a mean of $1,527. Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women.

At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women?

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