The time required for the first stage of an assembly line is normally distributed with a mean of 28 minutes and variance of 5 minutes, while the time required for an independent second stage is normally distributed with a mean of 17 minutes with a variance of 4 minutes. what is the probability that the two stages take more than 50 minutes?

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Moose

Mathematics

16 March, 07:57

The time required for the first stage of an assembly line is normally distributed with a mean of 28 minutes and variance of 5 minutes, while the time required for an independent second stage is normally distributed with a mean of 17 minutes with a variance of 4 minutes. what is the probability that the two stages take more than 50 minutes?

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Cierra Riddle · Answer 1

The mean for both processes is 28+17 = 45 minutes.

The variance is additive, so the total variance is 5+4 = 9. The standard deviation is the square root of variance, which is 3 minutes.

Then the z-score associated with a time of x = 50 minutes is:

z = (x - mean) / SD = (50 - 45) / 3 = 1.67

From a z-table, the probability that (z > 1.67) is 0.0475.