Refer to the Journal of Aqua cultural Engineering (Nov. 2012) study of the feasibility of laser scanning to estimate the volume of fish in a tank, Exercise 7.25. Recall that turbot fish were reared in a tank for experimental purposes and laser scans were executed in randomly selected locations in the tank, each scan providing an estimate of the volume (in kilograms) of fish layer. Determine the number of laser scans that must be executed in order to estimate the true mean volume of fish layer in the tank to within 5 kg with 95% confidence. Use the sample standard deviation obtained in the original study, 15 kg, as an estimate of the true volume standard deviation.

Data from Exercise 7.25

Engineers design tanks for rearing commercial fish to minimize both the use of natural resources (water) and the rearing volume necessary to ensure fish welfare. One key to a well-designed tank is obtaining a reliable estimate of the volume (biomass) of fish reared in the tank. The feasibility of a laser scanning technique for estimating fish biomass was investigated in the Journal of Aqua cultural Engineering (Nov. 2012). Fifty turbot fish were reared in a tank for experimental purposes. A laser scan was executed in four randomly selected locations in the tank and the volume (in kilograms) of fish layer at each location was measured. The four laser scans yielded a mean volume of 240 kg with a standard deviation of 15 kg. From this information, estimate the true mean volume of fish layer in the tank with 99% confidence. Interpret the result, practically.