11:18 PM g 'G)' I! Q 33 .ulll WP. .ulll '9' e Question 2 4 Marks The following table provides product survey results for the reliability rating of four mobile phone brands. A value of 0 represents completely unreliable and a value of 100 indicates completely reliable. Using the data in the table answer the following quations. Reliability Scores for Mobile Phone Brands Brand A Brand 8 Brand C Brand D 77 35 50 50 55 89 39 89 79 46 95 57 45 75 68 54 83 81 33 60 68 78 37 69 55 61 72 82 43 74 73 62 53 56 70 92 66 63 30 64 (a) Compute the mean, median, rst quartile, and third quartile for each brand. Use the exact position, (n+l)f, where n is the nLunber of observations and f is the relevant fraction for the quartile. 1 mark (b) Calulate the standard deviation, range and coefcient of variation from the data for each brand. 1 mark (0) Draw a box and whisker plot for the reliability of each brand and put them side by side on the same scale so that the reliability of the phones can be compared. 1 mark (d) Compare the box plots and comment on the distribution of the data. 1 mark 30f5 Question 3 4 Marks Players in a football league were surveyed using a simple random sample to nd their performance in relation to the amount of training they do through the week. 11:18PM QQDQ *dlllm'i'allll- e Question 3 4 Marks Players in a football league were surveyed using a simple random sample to nd their performance in relation to the amount of training they do through the week Training (hourst'week) 35 Performance If a player is chosen randomly from the league, answer the following questions based on the data in the table: (a) What is the probability that a player is training through the week? 1 mark (b) What is the probability that a player that trains more that ten hours per week will only achieve medium performance? 1 mark (c) What is the probability that a player will practice for 5 or more hours per week? 1 mark (d) What is the probability that a player will not train are will be a low performer? 1 mark 4of5 11:19PM QQDQ *dlllm'iallll e Question 4 4 Marks (a) A car company collected data and found that their brake pads lasted for a mean distance of 180 thousand kilometers with a standard deviation of 20 thousand kilometers. The data was found to be normally distributed. The supplier of the brake pads had specied the lifetime of the brake pads to be 150 thousand kilometers. (i) What percentage of brake pads will under perform? 1 Mark (ii) The car company has decided to specify the percentage of brake pads that under perform to 1%. What should the standard deviation need to be to meet this requirement? 1 mark (b) The annual income of car company workers on the production line was found to have a mean of $35,000 and a standard deviation of $6,000. lf random samples of 50 production line workers were taken from the production line, calculate the proportion of sample mean annual incomes that would exceed $37,500. I mark (c) The number of years of service of 10 car company production line workers varies uniformly between 5 years and 12.5 years. What is the probability that the length of employment for a production line worker is 10 years? 1 mark Question 5 4 Marks (a) The Department of Education found that only 55 percent of students attend school in a remote community. If a random sample of 500 children is selected, what is the approximate probability that at least 250 children will attend school? Use normal approximation of the binomial distribution. 1.5 marks (b) A hotel chain found that 120 out of 225 visitor who booked a room cancelled their bookings prior to the 24hr no reind period. Determine whether there is evidence that the population proportion of visitors who book their stay and cancel their bookings prior to the no refund period is less than 50% at a 1% condence level. 1.5 marks (c) The Queensland education department surveyed 1000 parents to assess those with having nancial hardship. It was determined that 19% of the parents suffered some nancial hardship of which 10% could not afford the full cost of their childs education. Construct a 99% condence interval for the proportion of parents who are suffering fmancial hardhip and cannot afford the full cost of their child's education. 1 mark 50f5