USE APPENDIX FORMULA AND STATISTICAL TABLES Correction*Soalan 1a)*Find the margin of error of this special examination if 25 samples are selected randomly to complete this exam, at 99% level of confidence.*Soalan 3a)*Find the margin of error of this calcium concentration measures at 95% level of confidence.
SMS1024: ELEMENTARY STATISTICS Answer ALL questions [40 marks] 1 . A special committee is set up by the university to design and administer a special examination, aiming to recognize students' emotional intelligence. The new examination format can be completed in an average time of 117 minutes, with standard deviation of 7 minutes. Assuming that the examination completion time, X is normally distributed. a. Find the margin of error of this special examination. [4 marks] b. Construct 99% confidence interval if 25 samples are selected randomly to complete this exam. [6 marks] 2. The spreading of the coronavirus disease (Covid-19) has caused a pandemic around the world. The average of a daily new cases around the world are about 411,688. This disease's distribution is skewed to the left with the mean of 411,688 new cases and the standard deviation of 10,033 new cases a day. a. Calculate the mean and standard deviation of the sampling distribution of this Covid-19 disease for a sample of 24 North American countries. Describe the shape of its sampling distribution. [4 marks] b. Calculate the mean and standard deviation of the sampling distribution of this Covid-19 disease for a sample of 50 Asian countries. Describe the shape of its sampling distribution. [4 marks] C. Compare the shape of these sampling distributions between part (a) and (b). Briefly explain. [2 marks] [See next page SMS1024: ELEMENTARY STATISTICS 3. Suppose that 100 samples of water from a fresh water lake are taken and the calcium concentration (milligrams per liter) is measured. It is known from the past data that the average of the calcium concentration is 0.66 mg/I and the standard deviation is 0.049 mg/. Find the margin of error of this calcium concentration measures. [4 marks] b. Construct 95% confidence interval for the population mean. [6 marks] 4. Food Panda Malaysia Managing Director claims that the average salary that riders could earn at least of RM7,000 per month depends on the potential area and order they have received. The salary is normally distributed with a standard deviation of RM5500 per month. A sample of 100 Food Panda riders are drawn from this population. a. Find the mean and standard deviation of the sampling distribution of sample means. [2 marks] b. What is the probability that the average salary of these riders will be less than RM6,500 per month? [3 marks] C. What is the probability that the average salary of these riders will be between RM7,200 to RM8,500 per month? [5 marks]
