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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 88.75 points? Find P(X > x) as a decimal.
Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0951. Find z to two decimals.
The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 22.4 and 42.8 min? Give P as a decimal.
The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 20% is to the right of it. Find the cut-off x.
The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.
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