1) Your parents are always complaining that you do not do enough housework. They say that you should be helping them out because you are only a student and you have alot more spare time than them. The number of hours per week that your parents work has a mean of 46.75 hours and a standard deviation of 2.59 hours. You believe that the number of hours per week that you have to study for university has a mean of 47.04 hours and a standard deviation of 2.52 hours.

You plan to record the number of hours that you study each week over 17 randomly selected weeks throughout the year. Calculate the probability that the mean of your sample is greater than the mean number of hours per week worked by your parents. Give your answer as a decimal to 4 decimal places.

2) Baggage allowances for passengers on "High Flying Airline" flights are for an average baggage weight of 25.00 kg with a standard deviation of 4.35kg. On a flight designed to seat 80 passengers, the maximum allowable weight of passenger baggage is 2066kg. Calculate the probability that on a randomly selected flight, the 80 passengers have baggage whose total weight exceeds the allowable limit. Give your answer as a decimal to 4 decimal places.

3) Menso is an organisation for people with hight Intelligence Quotients (IQs). Menso is investigating the average IQ of primary school students to determine whether its entry requirements should be altered for younger people. A sample of 73 primary school students have been randomly selected from schools throughout the country. The sample mean IQ of those studets was calculated as 100. It is known that the population standard deviation of IQs of all people is 13, and it is assumed that this standard deviation will also apply specifically to the IQs of the primary school students.

Calculate the width of the 90% confidence interval for the mean IQ of primary school students. Give your answer to 2 decimal places.

4) Badbury chocolates are planning on carrying out a quality assurance testing of their chocolate manufacturing process, specifically into the number of defective chocolates producted. The chief of quality control, Meticulous Martin, has declared that the distance between the sample mean and population mean should be no more than 900 chocolates during its testing process. Based on past testing, Martin believes that the population standard deviation of the number of defective chocolates produced by the company per year is equal to 5175. Meticulous Martin requires a confidence level of 99%.

Calculate the minimum sample size that should be used by Martin to ensure that the sample mean gained is no more than 900 units from the population mean with 99% confidence. Give your answer as a whole number.