1 of 2 ID: MST.FET.SD.SDI.01.0040A [3 marks] It is known that, across the adult population, the average number of words read per minute is 267 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: 267. You decide to survey 100 employees, and find that in this sample the average words per minute is 270.62. a) Based on the assumption that the population mean is 267 and that the population standard deviation is 22, calculate the z-score of the sample mean in your survey. Give your answer as a decimal to 2 decimal places. b) Determine the proportion of the standard normal distribution that lies to the right of this z-score. That is, determine the area to the right of this z-score in the standard normal distribution. You may find this standard normal table useful. Give your answer as a percentage to 2 decimal places. Area = % c) Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions: A: There is a chance of x% that your friend is correct, that the true population mean is 267. B: If your colleague is correct and the true population mean is 267, then x% of all samples will produce a sample mean of 270.62 or lower. C: If your colleague is correct and the true population mean is 267, then x% of all samples will produce a sample mean of 270.62 or higher. D: There is a chance of x% that the true population mean is 267 or lower. E: There is a chance of x% that the true population mean is 267 or higher. Select the statement that can be inferred from your findings: OA OB Oc OD OE 2 of 2 ID: MST.FET.SD.SDI.02.0030A [3 marks] You work on a traffic 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 875. 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 36. You randomly select 45 days on which to monitor the traffic going through this intersection. a) Complete the following statement by filling in the correct numbers. Give your answers to the nearest whole number of cars. If the true population mean really is 875, then for 95% of all samples of size n - 45, the sample mean will be somewhere between and cars b) Over the 45 days, you find that an average of 890 cars pass through the intersection. Therefore with 95% confidence you can rule out the possibility that your colleague's hypothesis was correct cannot rule out the possibility that your colleague's hypothesis was correct