QUESTION 1

1. Let A and B be independent events.Which of the following is always TRUE for these events?
2. A.P(A and B) = P(A) P(B)
3. B.P(A or B) = P(A) + P(B)
4. C.P(A given B) = P(B)
5. D.All of the above are always true

1 points

QUESTION 2

1. Suppose it is known that80%of a group are female,that52%of the group are smokers,and that40%of the group are both female and smokers.Suppose a randomly selected person from the group is a smoker.What is the probability that this person is a female(to the accuracy given)?
2. A.0.5
3. B.0.77
4. C.0.8
5. D.none of the above

1 points

QUESTION 3

1. It is known that P(A) = 0.3, P(B) = 0.6, P(A andB) = 0.15 and P(A orB) = 0.75. Given that B occurs what is the probability that A also occurs?
2. A.0.15
3. B.0.25
4. C.0.3
5. D.0.5

1 points

QUESTION 4

1. Occasionally businesses are selected for audit by a government department,as described by the following tree.They are initially identified as"high risk"(HR),"medium risk"(MR)or "low risk"(LR),and then audited(A)or not(A')as shown.Consider a randomly selected firm,and outcomes describing the risk classification and whether or not audit has occurred.What is the probability that the selected firm has not been audited?
3. A.0.045
4. B.0.185
5. C.0.2
6. D.0.385

1 points

QUESTION 5

1. Consider the following tree. What is the probability B occurs?
3. A.0.25
4. B.0.4
5. C.0.55
6. D.0.65

1 points

QUESTION 6

1. Consider the following tree. Which event is certain?
3. A.B
4. B.B, if A occurs
5. C.A or B
6. D.A and B

1 points

QUESTION 7

1. Consider the following tree. What is the probability A and B and C occurs?
3. A.0
4. B.0.168
5. C.0.832
6. D.1.3

1 points

QUESTION 8

1. Consider the following tree. What are the missing probabilities, and their labels?
3. A.,,
4. B.,,
5. C.,,
6. D.,,

1 points

QUESTION 9

1. If X is binomial with parameters n = 8 and p =0.54,what is P(X = 5)?Give your answer to 4decimal places.

1 points

QUESTION 10

1. If X is binomial with n = 8 and p =0.39, what is P(1 X 3)?Give your answer to 4decimal places.

1 points

QUESTION 11

1. If X is binomial with parameters n=21 and p=0.44,what is P(X <9)?Give your answer to four decimal places.

1 points

QUESTION 12

1. If X is binomial with parameters n=16 and p=0.45,what is P(X >6)?Give your answer to four decimal places.

1 points

QUESTION 13

1. If X ~ Bin(23,0.37), what is the mean of X?Enter your answer to 1dp

1 points

QUESTION 14

1. If X ~ Bin(12,0.35), what is the standard deviationof X?Enter your answer to 2dp

1 points

QUESTION 15

1. If X is binomial with 3trials and probability of success equal to 0.7,what is the mode of X?
2. A.0
3. B.1
4. C.2
5. D.3

1 points

QUESTION 16

1. If X ~ N(75,20²), what is P(X < 51)?Give your answer to four decimal places.

1 points

QUESTION 17

1. If X ~ N(23,8.1²), what is P(X > 16)?Give your answer to four decimal places.

1 points

QUESTION 18

1. If X is normal with mean 9.5 and standard deviation 6.1,what is P(0

1 points

QUESTION 19

1. If X is normal with mean 12 and standard deviation 5.3,what is P(4

1 points

QUESTION 20

1. If X is normal with mean 6.4 and variance 7.3, what is the probability that X is less than 5?Enter your answer to four decimal places.

1 points

QUESTION 21

1. If X is normal with mean 20.5and standard deviation 8.2, what is the 30th percentile of X?Give your answer to 1decimal place.

1 points

QUESTION 22

1. If X is normal with mean 32 and standard deviation 12,what is the lower quartile of X?Give your answer to one decimal place.

1 points

QUESTION 23

1. If X has mean 1.29 and standard deviation 0.53, what is P(X > 0)?
2. A.0.0075
3. B.0.4925
4. C.0.9925
5. D.unable to be calculated with the information given

1 points

QUESTION 24

1. What is the main reason the central limit theorem is so useful?
2. It tells us the sample mean is normal if the population is normal
3. It ensures we have large samples
4. It lets us use the normal distribution for the sample mean without specifying the distribution of the population
5. It ensure that the limit is in the centre of the distribution

1 points

QUESTION 25

1. Consider a discrete random variable X, with probability function given in the following table:
3. What is the mean of this random variable?
4. A.0.2
5. B.1.5
6. C.2
7. D.none of the above