need help for these basic probability quiz. thank you.

QUESTION 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	0.36	0.31	0.13	0.09	?

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

QUESTION 2

A recent study revealed that 60% of American drivers used their seatbelts. A sample of 20 drivers on a Florida freeway was selected. Let X be the number of drivers in the sample wearing a seatbelt.

a	X is not a binomial variable because the outcomes are not independent
b	X is not a binomial variable because the probability does not remain constant
c	X is a binomial variable because all four binomial properties are satisfied.
d	X is not a binomial variable because some of the binomial properties are not satisfied.

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 $2.1 million. If yearly sales are mediocre they can make a profit of $0.8 million. Finally, if yearly sales are low they can lose $1.6 million. The probability that yearly sales will be high is 0.34 and the probability that yearly sales will be mediocre is 0.4. Calculate the variance of profit for the new brand of makeup product (in $millions²). Give your answer to two decimal places.

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.

	Moved	Slack work	Abolished	Total
Male	U	V	650	3335
Female	W	792	520	X
Total	3051	Y	Z	6003

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.

a	29.7% of workers lost their jobs because of slack work
b	The probability a worker lost their job as a result of being female and the workplace moved was 0.282
c	72.7% of participants in the survey were female or lost their job because the workplace moved
d	Of the workers who lost their job because the position was abolished, 19.5% were male
e	Gender and the reason for job loss are independent

QUESTION 5

Sixty 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 28% of people will prefer Pepsi to Coke. Based on this claim, determine the probability (to 4 decimal places) that:

1. fewer than twenty-five participants prefer Pepsi

2. at least 22 people but no more than 30 participants preferred Pepsi