X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. 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 0.8315. Find z to two decimals.
The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 172.75 and 183.95 cm? Give P as a decimal.
The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 4 of them is below 99 kg. Round z to two decimals.
The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 40% is to the right of it. Find the cut-off x.
The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 5% is to the right of it. Find the cut-off x.
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