X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.
Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2296. Find z to two decimals.
X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 108.2 s. Round z to two decimals.
The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 26.3 and 37.1 min? Give P as a decimal.
The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 25% of them lie (the 25th percentile).
The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 60% is to the left of it. Find the cut-off x.
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