# Statistics

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t00788

Mathematics

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Please provide all working for the questions in the attached file.Statistics.pdf

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Q1 The local pizza take away randomly sampled seven customers on a Friday night and recorded the number of pizzas they ordered. The following data were obtained 20 3 2 6 1 3 3 (a) Compute the mean, median and modal number of pizzas ordered. (b) Which of the above measures in (a) is the most representative? Justify your answer. (max 100 words) (c) Compute the range, variance and standard deviation of the number of pizzas ordered. Q2 A manufacturer of a popular chocolate bar measures the weight of forty randomly selected bars at the end of the production line. The weights (in grams) are summarised in the following table: (a) Write a summary report for the manufacturer about the performance of the production line in terms of the weight of the chocolate bar produced. (Max 200 words) You are not required to comment on the shaded sections of the table. (b) The bars have a weight of 50g marked on their wrappers. Do the data suggest that the manufacturer is satisfying this requirement? Justify your decision using the Empirical Rule. Q3 A client has asked an investment adviser to report on the price/earnings ratios (P/E) of 30 selected companies. The data were summarised using a stem-and-leaf display and a Boxplot. (a) Write a short report for the client on the price/earnings ratios of these companies. (Max 200 words) Q4 The shelf life of a cake mix has a mound-shaped distribution with a mean of 275 days and a standard deviation of 55 days. (a) What percentage of cake mix packets remain fresh for 330 days or more? (b) Find the Z-score of a cake mix packet that remains fresh for 160 days. Comment on the relative position of this packet in the distribution. Q5 One thousand households in a city were surveyed to see if they will subscribe to a new pay television connection. The households were also classified as; low, medium or high income and the data are reported in the table below: Will Subscribe Low Income Medium Income High Income Yes 30 140 100 No 170 460 100 A household is selected at random from this population. (a) What is the probability that the household is a medium income household? (b) What is the probability that the household will subscribe to a new connection? (c) What is the probability that the household will not subscribe and has a low income level? (d) What is the probability that the household will not subscribe or has a low income level? (e) What is the probability that the household has a medium income if the household indicates it will subscribe to a new connection? (f) Are the events “the household has a medium income” and “the household indicates it will subscribe to a new connection” independent? State the reasons for your answer. (g) Are the events “the household has a low income level” and “the household will not subscribe” mutually exclusive? State the reasons for your answer. Q6 A large sample of over-50-year-old males was classified according to their health status and the adequacy of their retirement savings. The sample had 55% classified as being in poor health (P) and the rest were in good health (G). Of those in poor health, 30% were not saving adequately for retirement (N) and 80% of those in good health were saving adequately for retirement (S). (a) Construct the probability tree for this problem and calculate all the joint probabilities. (b) What is the probability that a randomly selected person is not saving adequately for retirement? (c) What is the probability that a randomly selected person is in good health given they are not saving adequately for retirement?
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