It is known that, across the adult population, the average number of words read per minute is 261 and the population standard deviation is 22. You work for a company with many employees across the country, and you would like to know what the average words per minute is for company employees. Your colleague proposes that he thinks the average will be the same as the average in the general population: 261. You decide to survey 100 employees, and nd that in this sample the average words per minute is 264.33. a) Based on the assumption that the population mean is 261 and that the population standard deviation is 22, calculate the zscore of the sample mean in your survey. Give your answer as a decimal to 2 decimal places. b) Determine the proportion ofthe standard normal distribution that lies to the right ofthis zscore. That is, determine the area to the right of this zscore in the standard normal distribution. You may nd this standard normal table useful. Give your answer as a percentage to 2 decimal places. Arapwa c) Denote by x% the percentage proportion you calculated in part b). Consider the following ve potential conclusions: A: There is a chance ofx% that your friend is correct, that the true population mean is 261. B: If your colleague is conect and the tIue population mean is 261, then x% of all samples will produce a sample mean of 264.33 or lower. C: If your colleague is correct and the true population mean is 261, then x% of all samples will produce a sample mean of 264.33 or higher. D: There is a chance of x% that the true population mean is 261 or lower. E: There is a chance of x% that the tIue population mean is 261 or higher. Select the statement that can be inferred from your ndings: You work on a tIafc management team for the city. There has been a proposal to add a new lane to a road near a busy intersection. As part of the research into whether or not to build the new lane, the team would like to know how many cars, on average, pass through this intersection at peak hour each day [5 pm to 6 pm). Your colleague has developed the hypothesis that the population mean is 823. You intend to test this hypothesis. For the purposes of this research, the team is assuming that the standard deviation in the number of cars passing through each hour is 35. You randomly select 42 days on which to monitor the tIaffic going through this intersection. a) Complete the following statement by lling in the correct numbers. Give your answers to the nearest whole number of cars. If the tIue population mean really is 873, then for 90% of all samples of size n = 42, the sample mean will be somewhere between \\:l and \\:l cars. b) Over the 42 days, you nd that an average of 878 cars pass through the intersection. Therefore with 90% condence you O can rule out the possibility that your colleague's hypothesis was correct 0 cannot rule out the possibility that your colleague's hypothesis was correct