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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?
0.4686 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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