Kirks Soft Drinks regularly check the performance of their soft drink bottle filling machines.From observations over many years, the company has concluded the fill amounts in their 2 litre bottles is normally distributed with a mean of2 litres and a standard deviation of0.17 litres.What fill amount (in litres) will see97% of all bottles contain less than this fill amount? (4 decimal places)

The average and standard deviation of the amount of Goods and Services Tax remitted by all performance artists in a twelve month period were $5.09 thous and $2.14 thousrespectively. If a sample of82 artists was taken, find the sample average value (in thous dollars) below which only 1% of taxes would lie.(2 decimal places)

Benford's Law is a probability rule frequently used by accounting auditors to detect systematic fraud. It states that approximately 19.1% of numbers will begin with the number 2.An auditor decides to investigate a particular firm further if a sample proportion of their invoices, with the invoiced number beginning with a 2, is in the highest 0.5% of all possible sample proportions.What sample proportion will cause further investigation of the firm if a random sample of 749 invoices is selected? Express youranswer in decimal form (ienot as a percentage),correct to two decimal places.

The general manager of a logistic consulting group believes that 22% of the firm's orders come from new customers. A simple random sample of 135 orders was selected.Using the manager's belief, determine:

1. The standard error for the sampling distribution of proportion.(4 decimal places)

2. The probability that at least 27% of the sample orders will be from new customers.(4 decimal places)