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4. Review questions with fully worked solutions

The first part of this section contains review questions to enable students to consolidate their understanding. They are grouped according to the Stats Means Business chapter to which they relate. The second part, section 4.2 contains the worked solutions to these questions, again organised by chapter.

1. Review questions

a) Chapter 1

1.1 Match the definitions listed below on the right to the words listed on the left.

(a) statistics (i) something that occurs by chance

(b) Statistics (ii) a subset of a population

(c) random (iii) a complete set of things to study

(d) sample (iv) a value of a variable that has occurred

(e) population (v) a set of numerical data

(f) observation (vi) the study of statistics

1.2 Match each of the symbols on the left to the definitions listed on the right.

(a) X (i) the number of observed values

(b) Σ (ii) the third in a set of observed

values of the variable X

(c) x (iii) a variable

(d) n (iv) a single observed value of the variable X

(e) x3 (v) the sum of

1.3 You have to fly from London to Tashkent. The plane is due to depart at 21.30 and the airline insists that you check in two hours before take off. You estimate that it will take an hour and a half to drive to the airport and a further 20 minutes to make your way from the car park to the check-in desk.

(a) What time should you start your journey to the airport?

(b) The flight is scheduled to take 6 hours 45 minutes. Going through passport control and collecting your baggage should take an hour. If local time is five hours ahead of UK time, by what time should the person who is meeting you aim to be at the airport in Tashkent?

1.4 A motoring journalist is studying the technical specification of a new car not yet available in the UK. The fuel economy is expressed in continental European style; according to the document the vehicle uses 7.3 litres of fuel per 100 kilometres travelled. What is the fuel economy of the car in miles per gallon? (There are 4.546 litres in a gallon and 1.609 kilometres in a mile, both to three decimal places.)

1.5 A UK businessman working in a developing Asian republic discovers that he can buy a new car from a local factory for 600 000 units of local currency, soom. The official exchange rate is 120 soom to one US dollar, but in the bazaars he can get 150 to the dollar. What is the cost of the car in pounds sterling if one dollar is worth 65 pence and

(a) he changes money at the official rate?

(b) he changes money in a bazaar?

1.6 The central feature of a new shopping centre is a square platform composed of one-metre square marble tiles.

(a) If the designer wants the platform to measure 14 metres by 14 metres, how many one-metre tiles will be required?

(b) If the budget is sufficient for only 175 of these tiles and the tiles cannot be cut, what are the dimensions of the largest square platform that can be assembled?

1.7 The promotional brochure produced by a Health Club informs us that ‘75 per cent of our members are under 30, and 60 per cent of our members who are under 30 are females’. If the Club has 900 members, how many of them are women under 30?

1.8 One third of a percent of the population of Glasburgh and a quarter of a percent of the population of Edingow record their occupation as ‘company director’. If the populations of Glasburgh and Edingow are three quarters of a million and 900,000 respectively how many company directors reside in each place?

1.9 A regulatory authority assesses the performance of railway operators on the proportion of trains that arrive late at their destinations. If more than one in twenty trains are late the operator receives a public warning. If more than one in five trains are late the operator is fined. The performance of the operators over the most recent review period is set out below:

|Operator |Total train journeys |Number of late arrivals |

|Ingenue |8497 |521 |

|Low Commotion |12038 |580 |

|Midlands Trainline |4277 |862 |

|Rock Island |10355 |512 |

|Union Specific |15273 |928 |

Work out the percentage of each operator’s trains that are late and identify those that will be warned and those that will be fined.

1.10 A visitor to Britain from Bahrain wants to buy some articles of clothing in a department store in London. He selects a man’s jumper costing £29.99, a lady’s cardigan that costs £34.99, and a pair of men’s shoes for £49.99. A large sign in the store says that visitors from abroad can buy goods ‘VAT-free’. The prevailing rate of VAT is 17.5 per cent. How much will he be charged for these goods?

1.11 An electricity supplier charges domestic consumers a fixed quarterly fee of £8.50 for maintaining the supply and 16.35 pence for each unit of electricity consumed. The total amount is then taxed at 5 per cent. A household uses 829 units of electricity in a quarter, how much will it be charged, including tax?

1.12 A single graduate is offered a job at a salary of £22 000 per annum. She would like to know how much pay she will receive per month after tax and National Insurance. She has obtained the following advice from her local tax office:

(a) A single person is entitled to a tax allowance of £5435. This must be subtracted from total pay to give the taxable pay.

(b) The taxable pay is taxed at 20 per cent.

(c) The National Insurance is 11 per cent of total pay, but is subtracted from the amount of pay after tax.

Work out how much her take-home will be per month.

1.13 A credit card company charges interest of 2.15 per cent per month on outstanding balances. A customer has no outstanding balance at the beginning of September. During September he spends £279 using his card and pays off £150 within the payment deadline. In October he spends £94 using his card.

(a) What is the amount he owes at the end of October?

(b) What is the minimum amount he will have to pay at the end of October if the company insists that 5 per cent of the balance must be cleared?

1.14 In one month consumers purchased 58749517 litres of bottled still mineral water. Of this total, sales of the three largest suppliers, in litres, were:

Vodder 6602362

Aquaria 5191584

Lake 4051948

(a) Specify the total sales and the sales of each of the suppliers to (i) four significant figures (ii) two significant figures

(b) Specify the market share of each of the suppliers to two decimal places.

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