Question 1 The following table shows the probabilities that a parole officer wil

Question

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: Number of violations 0 1 2 3 4 5 6 Probability 0.15 0.22 0.31 0.18 0.09 0.04 0.01 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

Explanation / Answer

Q1) Mean =0*0.15+1*0.22+2*0.31+3*0.18+4*0.09+5*0.04+6*0.01 = 2

Standard deviation = 1.37

Option C is Correct

Q2) Use Excel function

BINOM.DIST(3,7,0.30,FALSE) = 0.2269

Option B is Correct

Q3) Use Excel function

1-BINOM.DIST(1,10,0.60,TRUE) = 0.9983

Option C is Correct

Q4) Use Excel function

POISSON.DIST(4,6,FALSE)

= 0.1339

Option B is Correct

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