Scandals in Australian Sporting Clubs

Question 1 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 | 0 | 1 | 2 | 3 | 4 or more | Probability | 0.39 | 0.31 | 0.1 | 0.09 | ? |

Determine the probability that on a given day there are more than two interruptions to the system. (2 decimal places)

2 points
Question 2 1. The mean and standard deviation of a binomial distribution with n = 25 and p = 0.8 are | | 20 and 4 | | | 20 and 2 | | | 21 and 2 | | | 22 and 4 |
2 points
Question 3 1. 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 $2.9 million. If yearly sales are 'so so' they can make a profit of $0.6 million. Finally, if yearly sales are low they can lose $1.1 million. The probability that yearly sales will be high is 0.31 and the probability that yearly sales will be so-so is 0.41. 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 1. A group of participants was surveyed and the information collected shown in the partially completed contingency table below regarding gender and the attitudes on abortion. Firstly, calculate the missing values.

| Support | Oppose | Undecided | Total | Female | 291 | 275 | 38 | U | Male | 240 | 161 | 57 | 561 | Total | 531 | 436 | 95 | Z | 2.

3. 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. | | The probability that a participant opposed abortion was 46.3%. P(O) | | | The probability a participant was female and supported abortion was 0.25. (F n S) | | | The probability that a participant was P(male or undecided) about the issue of abortion was 51.4%. | P | | Gender and attitudes towards abortion are independent. [VERY UNSURE] | | | Of those surveyed who supported abortion, 42.8% were male. |
6 points
Question 5 1. A small plane has two engines which each have a probability of failing of 0.087. It is known that an engine is twice as likely to fail when the plane has only one engine working (ie. given one engine has failed). Determine the probability that both engines will fail. (3 dec pl)

2 points
Question 6 1. Given a binomial random variable with n = 60 and p = 0.36 find the probability of obtaining between 25 and 35 successes inclusive, to three decimal places.

3 points
Question 7 1. The probability a car is serviced under warranty is known to be 38% and the probability a car being a fully imported model is 32%. The probability a car is serviced under warranty and is a fully imported model is 8%. What is the probability a car is imported or serviced under warranty? (2 decimal places)

2 points
Question 8 1. To ascertain the effectiveness of a new diagnostic test for diabetes, a study was undertaken involving 883 participants, some of whom are independently known to actually have diabetes. A positive test result would indicate the presence of diabetes (with a negative test result indicating the absence of diabetes). The data collected to assess the effectiveness of this new test identified: * 301 participants known to actually have diabetes. * 24 participants who actually knew they had diabetes and where the test result was negative. * 535 participants with a negative test result.
A participant from the study is chosen at random. What is the probability the participant indicates a positive test result given they do not actually have diabetes? (3 decimal places)

2 points
Question 9 1. Previous studies have found 26% of all people prefer Coke to all other cola drinks. A random sample of 20 people is selected. What is the probability exactly three people in this sample prefer Coke? (3 decimal places)

3 points
Question 10 1. A Melbourne real estate agent lists two houses for lease in the same street, one built of brick and the other of timber. The agent estimates that the probability of being leased within one week is 0.75 for the brick and 0.68 for the timber house, and the probability of both being leased within one week is 0.52. If the timber house is leased within one week, what is the probability that the brick house is also leased within one week? Give your answer correct to three decimal places.

2 points
Question 11 1. The number showing on the upper face of a fair six-sided dice is observed when rolled. Consider events A and B defined as: not sure about the answers

* A = the number observed is at least 3 * B = the number observed is an odd number Find | 1. P(A') Blank 1 (3 decimal places) | | 2. P(A or B) Blank 2 (3 decimal places) |