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 0.0188. Find z to two decimals.
Drag z so that the shaded area between −z and z under the standard normal curve is 0.8293. Find z to two decimals.
The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 16 of them exceeds 632.8 g. Round z to two decimals.
The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 99% of them lie (the 99th percentile).
The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.
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