The table below provides counts from the data set for the variables Industry and Gender. Use the table to answer the following questions. i. Determine the probability that a superannuation account in the sample is from a Male account holder; ii. Determine the probability that an account in the sample is from a Male, given that the person works in Private industry; and iii. By considering the prior two probabilities, say if it appears that the variable Gender is independent of the variable Industry.
Question 1
A consultancy firm took a random sample of the accounts of a mid-sized superannuation fund that draws clients from across Australia. The firm’s aim was to investigate the size of superannuation balances in the fund for various client categories. Data on the first eleven accounts are shown below.
Recall the consultancy firm in Question 1 that took a random sample of the accounts of a mid-sized superannuation fund with clients across Australia to investigate the superannuation balances for various client categories. The table below provides counts from the data set for the variables Industry and Gender. Use the table to answer the following questions.
i. Determine the probability that a superannuation account in the sample is from a Male account holder;
ii. Determine the probability that an account in the sample is from a Male, given that the person works in Private industry; and
iii. By considering the prior two probabilities, say if it appears that the variable Gender is independent of the variable Industry. Justify your reasoning.
b. The annual yield (expressed as a percentage) for all investments in a particular asset class in the latest financial year was
i. Represent the probability that a randomly selected investment in this class will have an annual yield greater than 6.00%on a diagram and determine this probability.
ii. Represent the value for annual yield that only 10% of investments in this class exceed on a diagram and determine this value.
c. A retailer has 80% of its deliveries provided by Aussie Post and the remainder by Express Delivery. The retailer finds that 5% of Aussie Post deliveries are damaged, while this increases to 12% if the parcel is delivered by Express Delivery. In your analysis below use the notation A to represent the event that a parcel is delivered by Aussie Post and D to represent the event that a parcel is damaged.
i. Determine the probability that a delivery was not provided by Australia Post, that is()PA.
ii. Represent the situation describe as a probability tree with outcomes and probabilities labelled.
iii. Identify branches on your probability tree where a parcel is damaged and then calculate the proportion of all parcels that are delivered damaged.
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