For each of the following scenarios: • classify the variable as either numerical or categorical, AND • state whether the scale of measurement is nominal, ordinal, interval or ratio. (i) Fast food restaurants sell soft drinks in three sizes - small, medium and large. 1 mark (ii) A manufacturing company is sending millions of car parts overseas. 1 mark (b) Classify each of the following scenarios as a statistical problem in either descriptive statistics, probability or statistical inference. (i) Based on the survey conducted by Harris Green Pty Ltd, researchers predicted that group buying websites will be the most popular method for buying electrical and electronics products in the future. 1 mark (ii) A survey of 1000 adult drivers conducted by News Today shows that 45% of drivers admit to drinking and 36% admit to talking on the mobile phone while driving a vehicle. 1 mark Question 2 4 Marks The following data shows the service times (in seconds) for a sample of 96 customers who arrived at the service counter of a local hospital. 105 101 99 100 105 101 102 91 102 100 104 100 98 99 107 99 101 97 101 92 100 100 101 103 94 106 94 102 93 109 100 103 103 109 96 101 103 103 101 100 98 96 98 104 96 105 103 97 102 106 100 108 100 100 99 99 104 98 106 107 108 102 93 100 101 105 108 99 96 101 100 99 106 95 92 108 102 105 105 81 89 103 108 98 109 106 101 102 104 97 103 108 104 98 109 108 (a) Construct a stem-and-leaf diagram using this data. You need to generate between 5 and 10 stems only for the diagram. 1 mark (b) Draw a histogram for the frequency distribution with the first class "79 to less than 86". On the same graph draw the frequency polygon. 2 marks (c) Draw an ogive for the frequency distribution in Part (b) with the first class "79 to less than 86". 1 mark Question 3 4 Marks A health research agency has recently collected the following information when investigating the occurrences of skin cancer in a certain population of beach goers: • 7% of beach goers, who do not use any sun-screen lotion develop skin cancer at some stage in their life. • 1% of beach goers, who use sun-screen lotion develop skin cancer at some stage in their life. • 90% of beach goers use sun-screen. Use this information to answer the following questions. (Hint: construct a contingency table.) (a) If a beach goer is randomly selected, what is the probability that the person uses sun-screen lotion and yet develops skin cancer at some stage in life? 1 mark (b) If a beach goer is randomly selected, what is the probability that the person develops skin cancer at some stage in life? 1 mark (c) If a beach goer is randomly selected who has already developed skin cancer, what is the probability that the person does not use sun-screen lotion? 1 mark (d) What is the probability that a beach goer randomly selected will not develop skin cancer in life time or uses sun-screen lotion? 1 mark Question 4 4 Marks (a) A local supermarket receives fresh fruits delivery each morning at a time that varies uniformly between 6:00am and 8:00am. What delivery time can you be confident in stating that 95 percent of deliveries will arrive before? 1.5 marks (b) The maintenance department of a city's electric power company finds that it is cost-efficient to replace all street-light bulbs at once, rather than to replace the bulbs individually as they burn out. Assume that the lifetime of a bulb is normally (Gaussian) distributed with a mean of 8000 hours and a standard deviation of 300 hours. If the department wants no more than 3% of the bulbs to burn out before they are replaced, after how many hours should all of the bulbs be replaced? 1.5 marks (c) The time between unplanned shutdowns of an Internet service provider has an exponential distribution with a mean of 20 days. Find the probability that the time between two unplanned shutdowns is 13 days. 1 mark Question 5 4 Marks (a) The probability of success in a trial is 0.70. In 500 trials, what is the probability of succeeding between 280 and 355 times? Use normal approximation to the binomial distribution with continuity correction. 1 mark (b) Toyota requires a quality assurance check of new cars before a shipment is made. The tolerable exception rate for this internal control is 0.05. During an audit, 400 cars were sampled from a population of 4,000 cars, and 10 were found that violated the internal control. Calculate the upper bound for a 95% one-sided confidence interval estimate for the rate of noncompliance. 2 marks (c) BP wishes to estimate the mean amount of water that has seeped into the fuel storage tanks at its refineries in Sydney. A preliminary sample of n = 16 tanks showed that the standard deviation, s = 48 litres. How much larger should the sample be in order to estimate the mean water content of the tanks to within ±10 litres with 95% confidence? 1 mark we do not need any references for this assignment. its just that it has to be in one file.