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.
The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 574 h? Find P(X > x) as a decimal.
Drag z so that the shaded area between −z and z under the standard normal curve is 0.4313. 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 176.25 and 190.6 cm? Give P as a decimal.
The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 20% of them lie (the 20th percentile).
Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 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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