Please do pay extra attention to the decimal places and symbols.

QUESTION 1

The manager of Queensland Healths 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 0.35 0.3 0.1 0.06 ?

Determine the probability that on a given day there are more than two interruptions to the system.

__________(2 decimal places)

QUESTION 2

The mean and standard deviation of a binomial distribution with n = 25 and p = 0.8 are

1. a) 20 and 4

b) 20 and 2

c) 21 and 2

d) 22 and 4

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 $2.4 million. If yearly sales are mediocre they can make a profit of $1.2 million. Finally, if yearly sales are low they can lose $1.6 million. The probability that yearly sales will be high is 0.31 and the probability that yearly sales will be mediocre is 0.49. 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.

Closed Slack work Abolished Total

Male U V 595 3673

Female W 628 647 X

Total 2995 Y Z 6217

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 (can be more than 1 answer): _______________

a)

a) The probability that a worker lost their job as a result of being female and the workplace was closed was 0.204.

b) 68.7% of workers lost their job as a result of being female or the workplace was closed.

c) Of the workers who lost their job because the position was abolished, 47.9% were male.

d) The proportion of being male workers and losing their job for reasons other than slack work was 0.368.

e) Gender and the reason for job loss are independent

6 points

QUESTION 5

Fifty-five 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 39% of people will prefer Pepsi to Coke. Based on this claim, determine the probability (to 4 decimal places) that:

1. fewer than twenty-six participants prefer Pepsi

2. more than 26 but no more than 32 people prefer Pepsi

3 points

QUESTION 6

Suppose X and Y are independent events with marginal probabilities of 0.34 and 0.77 respectively. What is the probability that event X or Y occurs? (3 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 909 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:

301 of the participants confirmed they actually had diabetes, with the other participants confirming they actually did not have diabetes.

13 participants actually had diabetes and produced a negative test result.

535 participants produced 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 8

The industry standards suggest that 13% of new vehicles require warranty service within the first year. A dealer sold 16 Nissans yesterday. What is the probability that 3 of these vehicles require warranty service? (3 decimal places)

3 points

QUESTION 9

Along the road near Bundamba State High School, there are traffic lights at two different locations. At the first location, the light is green 80.9% of the time. At the second location, the light is green 79.9% of the time. The probability a vehicle gets a green light at the first location and the second location is 71.4%. What is the probability that the light will be green at the second location if the light was green at first location? (3 decimal places)

2 points

QUESTION 10

The numbers showing on the upper faces of two, fair, six-sided dice are observed when rolled.

Consider events A and B defined as:

• A = the sum of the two values observed on the upper faces is at least 8

• B = at least one dice has a 2 or less on the upper face

Find 1. P(B) (3 decimal places)

2. P(A or B) (3 decimal places)

QUESTION 1

The manager of Queensland Healths 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 0.35 0.3 0.1 0.06 ?

Determine the probability that on a given day there are more than two interruptions to the system.

__________(2 decimal places)

QUESTION 2

The mean and standard deviation of a binomial distribution with n = 25 and p = 0.8 are

1. a) 20 and 4

b) 20 and 2

c) 21 and 2

d) 22 and 4

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 $2.4 million. If yearly sales are mediocre they can make a profit of $1.2 million. Finally, if yearly sales are low they can lose $1.6 million. The probability that yearly sales will be high is 0.31 and the probability that yearly sales will be mediocre is 0.49. 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.

Closed Slack work Abolished Total

Male U V 595 3673

Female W 628 647 X

Total 2995 Y Z 6217

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 (can be more than 1 answer): _______________

a)

a) The probability that a worker lost their job as a result of being female and the workplace was closed was 0.204.

b) 68.7% of workers lost their job as a result of being female or the workplace was closed.

c) Of the workers who lost their job because the position was abolished, 47.9% were male.

d) The proportion of being male workers and losing their job for reasons other than slack work was 0.368.

e) Gender and the reason for job loss are independent

6 points

QUESTION 5

Fifty-five 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 39% of people will prefer Pepsi to Coke. Based on this claim, determine the probability (to 4 decimal places) that:

1. fewer than twenty-six participants prefer Pepsi

2. more than 26 but no more than 32 people prefer Pepsi

3 points

QUESTION 6

Suppose X and Y are independent events with marginal probabilities of 0.34 and 0.77 respectively. What is the probability that event X or Y occurs? (3 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 909 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:

301 of the participants confirmed they actually had diabetes, with the other participants confirming they actually did not have diabetes.

13 participants actually had diabetes and produced a negative test result.

535 participants produced 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 8

The industry standards suggest that 13% of new vehicles require warranty service within the first year. A dealer sold 16 Nissans yesterday. What is the probability that 3 of these vehicles require warranty service? (3 decimal places)

3 points

QUESTION 9

Along the road near Bundamba State High School, there are traffic lights at two different locations. At the first location, the light is green 80.9% of the time. At the second location, the light is green 79.9% of the time. The probability a vehicle gets a green light at the first location and the second location is 71.4%. What is the probability that the light will be green at the second location if the light was green at first location? (3 decimal places)

2 points

QUESTION 10

The numbers showing on the upper faces of two, fair, six-sided dice are observed when rolled.

Consider events A and B defined as:

• A = the sum of the two values observed on the upper faces is at least 8

• B = at least one dice has a 2 or less on the upper face

Find 1. P(B) (3 decimal places)

2. P(A or B) (3 decimal places)

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