Chapter 5.3, Problem 5.29ACI

Levelness of concrete slabs. Geotechnical engineers use water-level “manometer” surveys to assess the levelness of newly constructed concrete slabs. Elevations are typically measured at eight points on the slab; of interest is the maximum differential between elevations. The Journal of Performance of Constructed Facilities (February 2005) published an article on the levelness of slabs in California residential developments. Elevation data collected for more than 1 ,300 concrete slabs before tensioning revealed that maximum differential, x, has a mean of µ = .53 inch and a standard deviation of σ = .193 inch. Consider a sample of n = 50 slabs selected from those surveyed and let $\bar{x}$ represent the mean of the sample.

1. a. Fully describe the sampling distribution of $\bar{x}$.
2. b. Find $P\left(\bar{x}\succ .58\right)$.
3. c. The study also revealed that the mean maximum differential of concrete slabs measured after tensioning and loading is µ = .58 inch. Suppose the sample data yield $\bar{x}$ = .59 inch. Comment on whether the sample measurements were obtained before tensioning or after tensioning and loading.