1. An on-line retailing firm conducts a study into the number of on-line purchases of footwear made during all of last year. The study wants to determine the proportion of Australians over the age of 25 who purchase footwear on-line. The managing director of the on-line retailing firm believes this proportion of Australians is 23%. A random sample of 170 Australians over the age of 25 is selected. If the managing director's claim is true, what is the sample proportion value below which 10% of all sample proportions would exist? Express your answer correct to two decimal places.
2. The average and standard deviation of the amount of Goods and Services tax remitted by performance artists in a twelve month period were $7.895 thousand and $1.744 thousand respectively. If a sample of 50 artists was chosen, find the sample average value above which only 5% of sample averages would lie. Give your answer in dollars (to the nearest dollar).
3. If a variable is normally distributed, with a probability of 99.74% of occurring, how many standard deviations does this cover either side of the mean?
a) 2.57
b) 3
c) 5
d) 6
4. The marks on a midterm test are normally distributed with a mean of 72.3 and a standard deviation of 10.2. Find the probability that a class of 38 has an average less than 70.
5. A study measured the amount of consultation time physicians took with patients. From the study, it was determined that the consultation time was normally distributed with a mean of 15 minutes and a standard deviation of 2 minutes. What is the probability that the doctor will spend more than 11 minutes? Select from the answers below.