A precision automated nozzle dispenses a volume VVV ml of a chemical reagent, where VVV is modeled as a continuous random variable uniformly distributed on the interval [k−1.5,k+4.5][k - 1.5, k + 4.5][k−1.5,k+4.5], where kkk is a calibration constant.
A quality control audit takes a random sample of 80 dispensations, yielding a sample mean volume of vˉ=42.6\bar{v} = 42.6vˉ=42.6 ml.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean volume Vˉ\bar{V}Vˉ.
Hence, find a 98% confidence interval for kkk. Give the limits of your interval to 3 significant figures.