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- This topic has 1 reply, 1 voice, and was last updated 1 year ago by John Moffat.

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- February 28, 2021 at 10:37 am #612092
The weights of component X are normally distributed. The mean weight is 5,200kg and the standard

deviation is 430kg.

What is the probability of a component X weighing more than 6,000kg?

? 0.0314

? 0.2343

? 0.4686

? 0.9686i can’t understand this question and its explanation

Explanation is so:Using z = ??

x –

z =

6,000 – 5,200

430

z = 1.86

z = 1.86 corresponds to an area of 0.4686. However, we are interested in the shaded area =

0.5 – 0.4686 = 0.0314.

If you selected 0.2343, you divided the probability obtained (0.4686) by 2 instead of subtracting

it from 0.5.

If you selected 0.4686, you forgot to subtract 0.4686 from 0.5.

If you selected 0.9686, you added 0.4686 to 0.5 instead of subtracting it.z = 1.86 corresponds to an area of 0.4686 –i can’t understand this sentence

1.86 corresponds to an area of 0.46 ?? but why what is logic of this?

February 28, 2021 at 2:50 pm #6121300.4686 comes from the tables provided in the exam and means that 0.4686 (or 48.86%) of the area under the curve lies been 5,200 and 6,000 kg. This in turn means that the is a probability of 0.4686 that a component weight between 5,200 and 6,000 kg.

I explain how to use the tables and the logic behind it all in my free lectures on the normal distribution.

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