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Government regulations indicate that the total weight of cargo in a certain kind of airplane cannot exceed 330 kg. On a particular day a plane is loaded with 100 boxes of goods. If the weight distribution for individual boxes is normal with mean 3.2 kg and standard deviation 7 kg, what is the probability that the regulations will NOT be met:(a)- 1.5% (b)- 92% (c)- 8% (d)- 15% (e)- 85%

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Answer:

The probability that the regulations will NOT be met is (c)- 8%

Step-by-step explanation:

The standard deviation information in the question is wrong. It is not 7, It should be 0.7

the probability that the regulations will NOT be met for the plane loaded with 100 boxes of goods is

=P(X>3.3 kg) where 3.3 is the mean weight of the 100 boxes in the plane.

=P(z>z*) where z* is the statistic of 3.30 kg in the weight distribution.

z* can be calculated as

z*=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where

  • X  is the cutoff mean weight of the boxes the airplane cannot exceed (3.3 kg)
  • M is the mean weight of the boxes (3.2)
  • s is the standard deviation (0.7 kg)
  • N is the sample size (100)

then z*=[tex]\frac{3.3-3.2}{\frac{0,7}{\sqrt{100} } }[/tex] ≈ 1.43

then P(z>z*)≈0.08 or 8%

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