X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.
Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1539. Find z to two decimals.
The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 10 of them is below 812.1 kg. Round z to two decimals.
The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 244.25 and 257.75 g? Give P as a decimal.
The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 90% is to the left of it. Find the cut-off x.
Hole diameters D are normal with mean 25.04 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.
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