Acompany produces a women's bowling ball that is supposed to weigh exactly 14 pounds. unfortunately, the company has a problem with the variability of the weight. in a sample of 7 of the bowling balls the sample standard deviation was found to be 0.64 pounds. construct a 95% confidence interval for the variance of the bowling ball weight. assume normality. a) what is the lower limit of the 95% interval? give your answer to three decimal places. b) what is the upper limit of the 95% interval? give your answer to three decimal places. c) which of the following assumptions should be checked before constructing the above confidence interval? the data need to follow a normal distribution the data need to have small variance the data need to follow a chi-square distribution the data need to be right skewed

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?