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A random survey of university students was completed to estimate the proportion of students with a personal computer at home. In this survey, 1008 out of 1120 students responded that they did have a personal computer at home.  
(a) If there is no reason to believe that one student’s response influences another, estimate, with 98% confidence, the population proportion of students with a personal computer at home.   
(b)  Check the procedure you used in part (a) is appropriate by checking all the necessary conditions, assumptions and/or ‘rules of thumb’.  
(c) At the 98% confidence level, the company commissioning the survey would like to have a margin of error which is no more than 1%. What sample size is required in this case? (Use the conservative method when determining the required sample size)   
Question 2
The average sodium content per packet of a certain brand of soup in a cup is 780 milligrams and the standard deviation is 45 milligrams. Assume that the sodium content in this variety of soup in a cup is normally distributed.  
(a) (4 marks) If a single pack of soup in a cup is selected, find the probability that the sodium content will be less than 760 milligrams.  
(b) (4 marks) For random samples of 50 such packets of soup in a cup, state the sample distribution of the sample mean (specify the name of the distribution and the parameters of the distribution)?  
(c) (6 marks) If a random sample of 50 packets of soup in a cup is selected, find the probability that the mean sodium content will be more than 760 milligrams  



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