The compressive strength of a concrete is a normally distributed quantity with standard deviation 7.9. In an effort to improve the quality of the concrete compressive strength, measurements were taken on 30 specimens. For these specimens the mean was found to be 56.2. 1a). Find the 95% confidence interval for the mean compressive strength for the concrete based on the sample of 30 specimens. (0.5 marks) 1b). How many specimens should be sampled to be 95% confident that the 95% confidence interval for µ will contain the maximum error of 0.8? (0.5 marks) Hint and Instruction: – (1a) Use the Excel worksheet: CIE sigma known_Template. You may refer to Chapter 8 Excel Guide EG8.1 – EG8.4 In-Depth Excel on page 302 – 303 of the textbook. – (1b) Use the Excel worksheet: Sample Size Mean_Template. You may refer to Chapter 8 Excel Guide EG8.1 – EG8.4 In-Depth Excel on page 302 – 303 of the textbook You are also required to present your manual calculations, using the Standard Normal Probability table (Z table). You may present you calculations either in typeset or hand-written. Question 2 (4 marks) Among 18 patients with mitral stenosis and third heat sounds, the following heart rates were observed (Source: Wm. H. Gamble and P.S. Reddy. “Preservation of the third heat sound in mitral stenosis.” New England Journal of Medicine, V.308, No. 19, 1983, 498-502.). 80, 88, 57, 92, 60, 96, 53, 80, 86, 76, 110, 96, 86, 91, 83, 72, 67, 90 2a) Construct the box-whisker’s plot and the normal probability plot to justify that the sample data distribution can be considered approximately normal. (1.3 marks) 2b) Find the sample mean and standard deviation using Excel. (0.2 marks) 2c) Obtain the 95% confidence interval for the population mean heart rate

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