1 The manager of Queensland Health's computer network constructed the probability distribution for the number of interruptions to the system per day using historical data: Interruptions per day Probability 0 0.36 1 0.31 2 0.13 3 0.09 4 or more ? Determine the probability that on a given day there are more than two interruptions to the system. (2 decimal places) 2 points QUESTION 2 A recent study revealed that 60% of American drivers used their seatbelts. A sample of 20 drivers on a Florida freeway was selected. Let X be the number of drivers in the sample wearing a seatbelt. X is not a binomial variable because the outcomes are not independent X is not a binomial variable because the probability does not remain constant X is a binomial variable because all four binomial properties are satisfied. X is not a binomial variable because some of the binomial properties are not satisfied. 2 points QUESTION 3 Ester Ltd. is planning to launch a new brand of makeup product. Based on market research, if yearly sales are high they can make a profit of $2.1 million. If yearly sales are mediocre they can make a profit of $0.8 million. Finally, if yearly sales are low they can lose $1.6 million. The probability that yearly sales will be high is 0.34 and the probability that yearly sales will be mediocre is 0.4. Calculate the variance of profit for the new brand of makeup product (in $millions2). Give your answer to two decimal places. 2 points QUESTION 4 A group of participants was surveyed and the information collected shown in the partially completed contingency table below regarding gender and the reasons for job loss. Firstly, calculate the missing values. Male Moved U Slack work V Abolished 650 Female Total W 3051 792 Y 520 Z Now, using the completed contingency table, select the statements from the following list that are true. Note: a statement is true only if the value you calculated from the completed contingency table, when rounded to the same number of decimal places as in the statement, is the same as the value in the statement. 29.7% of workers lost their jobs because of slack work The probability a worker lost their job as a result of being female and the workplace moved was 0.282 72.7% of participants in the survey were female or lost their job because the workplace moved Of the workers who lost their job because the position was abolished, 19.5% were male Gender and the reason for job loss are independent 6 points QUESTION 5 Sixty people are recruited to participate in a Pepsi versus Coke taste test trial. The trial participants will be asked to taste a sample of both Pepsi and Coke (in a random order) and then to indicate which sample they prefer. Prior to performing this taste test trial, the researcher claims that 28% of people will prefer Pepsi to Coke. Based on this claim, determine the probability (to 4 decimal places) that: 1. fewer than twenty-five participants prefer Pepsi 2. at least 22 people but no more than 30 participants preferred Pepsi 3 points QUESTION 6 The probability a car is serviced under warranty is known to be 36% and the probability a car being a fully imported model is 25%. The probability a car is serviced under warranty and is a fully imported model is 10%. What is the probability a car is imported or serviced under warranty? (2 decimal places) 2 points QUESTION 7 To ascertain the effectiveness of a new, quicker, and simpler test for identifying diabetes, a study was undertaken involving 883 participants. With this test, a positive result indicates the presence of diabetes. A negative result indicates the absence of diabetes. Data collected to assess the effectiveness of this new test revealed: 318 of the participants knew they had diabetes, with the other participants definitely not having diabetes. 21 participants knew they had diabetes and produced a negative test result. 522 participants produced a negative test result. A participant from the study is chosen at random. What is the probability the participant does not actually have diabetes given the test result is positive? (3 decimal places) 2 points QUESTION 8 The industry standards suggest that 23% of new vehicles require warranty service within the first year. A dealer sold 24 Nissans yesterday. What is the probability that 3 of these vehicles require warranty service? (3 decimal places) 3 points QUESTION 9 Consider two events X and Y that have marginal probabilities of 0.69 and 0.52 respectively. Their joint probability is 0.46. Calculate the probability that event X occurs if Y has occurred. (3 decimal places) 2 points QUESTION 10 The number showing on the upper face of a fair six-sided dice is observed when rolled. Consider events A and B defined as: A = the number observed is at most 2 B = the number observed is an even number Find 1. P(A') 2. P(A or B) (3 decimal places) (3 decimal places)