Explain how collecting mean values (x-bar) from samples drawn from a dataset, regardless of the statistical distribution of the dataset, results in a distribution of those values that is centered on the mean value of the original dataset and is approximately normally distributed depending upon the sample size used. include the name the theorem that describes this phenomenon, and discuss what it means to treat the x-bar data points derived from sampling as a new random variable. why is this important in engineering?

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.