1 of 3 ID: MST.FET.SD.SDM.01.0040A [3 marks] A company provides tuition for mathematics students across the country. It provides two levels of tuition: tuition for general-level students and tuition for advanced- level students. All students who receive tuition at this company must first complete a test, to assess their initial comprehension of mathematics. For general-level students, the population mean score in this test is 50.77, with a population standard deviation of 11.24. For advanced students, the population mean score in the test is 81.62, with a population standard deviation of 16.69. A statistician wants to study the results of a random selection of general students and a random selection of advanced students. The statistician intends to draw a sample of 50 general-level students and a sample of 200 advanced-level students. a) From the following list, select the items that are relevant to calculating the extent to which the sample means vary, for samples from a population. the mean of the underlying population the variance of the underlying population the size of the samples collected b) For the samples described in the scenario above, the sample mean scores for samples of general-level students will have a |level of variation than the variation in sample mean scores for samples of advanced-level students. -2 of 3 ID: MST.FET.SD.SDM.02.0010A [1 mark] During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bottle follows a normal distribution with mean 20 fl oz and standard deviation 0.17 fl oz. The Fantra quality testing department has just carried out a routine check on the average amount of soft drink poured into each bottle. A sample of 25 bottles were randomly selected and the amount of soft drink in each bottle was measured. The mean amount of soft drink in each bottle was calculated to be 19.91 fl oz. The Fantra Chief Executive Officer believes that such a low mean is not possible and a mistake must have been made. Calculate the probability of obtaining a sample mean below 19.91 fl oz. You may find this standard normal table useful. Give your answer as a decimal to 4 decimal places. p 3 of 3 ID: MST.FET.SD.SDM.03.0030A [1 mark] A particular population has a mean of 197 and a variance of 1,030. Considering the sampling distribution of sample means of all samples of size 30, calculate the value of the sample mean for which 90% of samples have a sample mean less than this value. You may find this standard normal table useful. Give your answer to 1 decimal place. Sample mean =