Question 1: The following table shows the probabilities that a parole officer will receive 0, 1, 2, 3, 4, 5 or 6 reports of parole violations on any given day:

The expected value and standard deviation are

(a) 3, 2

(b) 2, 1.9

(c) 2, 1.37

(d) 2, 5.9

(e) 3, 0.18

Question 2: In a certain city credit card debt is responsible for 30 percent of all personal bankruptcies. What is the probability that three of the next seven personal bankruptcies filed in that city will be due to credit card debt?

(a) 0.027

(b) 0.2269

(c) 0.3

(d) 0.7731

(e) 0.0065

Question 3: A study shows that 60 percent of families in Rockhampton have a computer. Find the probability that amongst 10 families randomly selected that 2 or more will have computers.

(a) 0.9999

(b) 0.36

(c) 0.9983

(d) 0.0106

(e) 0.0017

Question 4: A bank receives on average 6 bad cheques per day. Assuming the distribution is Poisson, find the probability that the bank will receive four bad cheques on a given day.

(a) 0.8661

(b) 0.1339

(c) 0.1042

(d) 0.1954

(e) 0.2851

Question 5: A bank receives on average 2 bad cheques per day. Assuming the distribution is Poisson, find the probability that the bank will receive two or more bad cheques over a two day period.

(a) 0.0916

(b) 0.5940

(c) 0.4060

(d) 0.9084

(e) 0.1465

Question 6: The total area under a continuous probability distribution curve

(a) will vary depending on the application.

(b) will always be between 0 and 1.

(c) will always be exactly 1.

(d) can never be determined exactly.

(e) None of the above.

Question 7: The time a student waits to catch a bus in Rockhampton varies uniformly between 6 and 12 minutes. The probability that a particular student waits more than 7 minutes is:

(a) 0.833

(b) 0.6

(c) 0.666

(d) 0.333

(e) 0.5833

Question 8: Suppose the distribution of personal daily water usage in Rockhampton is normally distributed with a mean of 110 litres and a standard deviation of 24 litres. What is the probability that a person uses more that 120 litres of water?

(a) 0.8372

(b) 0.6628

(c) 0.3372

(d) 0.1628

(e) 0.6744

Question 9: The amount of instant coffee that a filling machine puts into "120 grams" jars varies from jar to jar and is normally distributed with a standard deviation of 2 grams. If only 2 percent of jars are to contain less than 120 grams of coffee, what must be the approximate mean weight of these jars?

(a) 115.9

(b) 120

(c) 117.9

(d) 122.1

(e) 124.1

Question 10: A television network claims that its Friday night movie regularly has 42 percent of the total viewing audience. If this claim is correct, what is the probability that among 500 Friday nights, at least 250 will be watching the movie? (Use the continuity correction)

(a) 0.58

(b) 0.5

(c) 1

(d) 0

(e) 0.42

Question 11: A stratified random sample is characterised by

(a) random selection of strata included

(b) all strata being represented in the sample in proportion to their representation in the population

(c) all members of selected strata being included in the sample

(d) the same number of members selected from each strata

(e) all the above

Question 12: Which of the following is a correct statement about the sampling distribution of X^-?

(a) The mean of the sampling distribution is always equal to the population mean.

(b) The means of all the samples are equal.

(c) The standard deviation of the sampling distributions is always equal to the population standard deviation divided by the square root of n.

(d) The shape of the sampling distribution is always approximately normal.

(e) None of the above are correct statements.

Question 13: An investor wants to buy a chain of supermarkets. Before the deal is finalised the investor wants to have some assurance that the chain of supermarkets will be a consistent money maker. The management of the chain of supermarkets claims that each store's profits have an approximately normal distribution with the same mean and a standard deviation of $12 000. If the management of the chain of supermarkets is correct, what is the probability that in a sample of nine supermarkets, the average profit will fall within $2000 of the actual mean?

(a) 0.3830

(b) 0.4772

(c) 0.0456

(d) 0.0912

(e) Unknown, since n < 30.

Question 14: The auditor for a large bank in Australia knows that the monthly balance of any given customer is $112 on average and the standard deviation is $56. If the bank selects 49 accounts, what is the probability that the sample average monthly balance is between $100 and $130?

(a) 0.079

(b) 0.9878

(c) 0.921

(d) 0.9332

(e) Cannot be determined unless the monthly balance of any given customer account is normally distributed

Question 15: The auditor for a large bank in Australia knows that the monthly balance of any given customer account is $112 on average and the standard deviation is $56. If the bank selects nine (9) accounts, what is the probability that the sample average monthly balance is below $100?

(a) 0.6428

(b) 0.7611

(c) 0.2611

(d) 0.7389

(e) Cannot be determined unless the monthly balance of any given customer account is normally distributed

Questions 16 and 17 refer to the following information:

The following data pertain to the amount of time (in minutes) taken by a accountant to complete client interviews

8   12   26   10   23   21   16   22   18   17   36   9

Assume times are approximately normally distributed

Question 16: The point estimates for a-and p respectively are:

(a) 7.77 & 18.16

(b) 60.30 & 18.16

(c) 60.30 & 12

(d) 8.11 & 18.16

(e) Cannot be determined as n < 30.

Question 17: What is the 98 percent confidence interval for the population mean?

(a) 11.80 & 24.53

(b) 14.97 & 21.36

(c) 12.07 & 24.26

(d) -29.15 & 65.48

(e) Cannot be determined as n < 30.

Question 18: For the Rockhampton Cement Company, a sample of 81 bags of cement had a mean X^- of 150 kg and a standard deviation of 12kg. The 95 percent confidence limits for the sample mean are approximately given by:

(a) 136 kg & 164 kg,

(b) 126 kg & 174 kg

(c) 147 kg & 153kg

(d) 116 kg & 184 kg

(e) Cannot be determined unless the number of investments is normally distributed.

Question 19: In evaluating the effectiveness of the state rehabilitation program, a survey of 49 prisoners (several thousand prisoners in prison) found that 35 percent were repeat offenders. What is the 90 percent confidence interval for the proportion of repeat offenders among the prisoners?

(a) 0.22 & 0.48

(b) 0.52 & 0.78

(c) 0.54 & 0.76

(d) 0.22 & 0.46

(e) Cannot be calculated.

Question 20: A manufacturer of fishing rods makes their rods from a composite material that is baked for a given amount of time and at a given temperature. The standard deviation of the breaking strength of the rods is 2.25 kg. What size sample must be taken in order that the total width of the 95% confidence interval for the population mean will not be greater than 0.3 kg?

(a) 3458

(b) 865

(c) 441

(d) 217

(e) 30

Need the answers from 11-20 without explanation.