Applications of sample mean probabilities 5.25, for a and b only. You do not need to interpret.

a. What is ur? c. Find P(x > 1.52 ). b. What is or? f. Would your answers to parts a-e change if the rates (c) c. Describe the shape of the sampling distribution of . of return on the investment for two consecutive years d. Find the z-score for the value x = 86.660. was not normally distributed? Explain. c. Find P(X > 86.660). 5.29 Levelness of concrete slabs. Geotechnical engineers use 5.25 Corporate sustainability of CPA firms, Refer to the Business water-level "manometer" surveys to assess the levelness mid Society (March 2011) study on the sustainability behav- of newly constructed concrete slabs Elevations are typi- for of CPA corporations, Exercise 1.28 (p. 51). Corporate cally measured at cight points on the slab; of interest is sustainability, recall, refers to business practices designed the maximum differential between elevations The Journal around social and environmental considerations The level of Performance of Constructed Facilities (February 2005) of support senior managers have for corporate sustainability published an article on the levelness of slabs in California was measured quantitatively on a scale ranging from 0 to 160 residential developments. Elevation data collected for points The study provided the following information on the more than 1,300 concrete slabs before tensioning revealed distribution of levels of support for sustainability; a = 68. that maximum differential, x, has a mean of at = .53 inch o = 27. Now consider a random sample of 45 senior manag- and a standard deviation of o = .193 inch. Consider a ers and let & represent the sample mean level of support. sample of # = 50 slabs selected from those surveyed and a. Give the value of ur. the mean of the sampling distribu- let x represent the mean of the sample. tion of x, and interpret the result. a. Fully describe the sampling distribution of J. b. Give the value of or. the standard deviation of the sam- b. Find P(X > .58). pling distribution of x, and interpret the result. c. The study also revealed that the mean maximum dif- c. What does the Central Limit Theorem say about the ferential of concrete slabs measured offer tensioning shape of the sampling distribution of X? mid loading is a = .58 inch. Suppose the sample data d. Find P(x > 65). yield x = .59 inch. Comment on whether the sample 5.26 Critical-part failures in NASCAR vehicles, Refer to The measurements were obtained before tensioning or after Sport Journal (Winter 2007) analysis of critical-part fail- tensioning and loading