Calculate a normal probability and determine an unknown standard deviation.

Calculate a normal probability and determine an unknown standard deviation.

6 marks
ProbabilityQuestionBank.pdf

The heights, H, of the people in a certain town are normally distributed with mean 170 cm and standard deviation 20 cm.

  1. A person is selected at random. Find the probability that his height is less than 185 cm.[3]
  2. Given that \(P(H > d)\) = 0.6808, find the value of d.[3]

Solution:

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Answer:\(P(H>d)=0.6808\) means \(P(H\le d)=0.3192\), with \(z\approx-0.47\). Thus \(d=170-0.47(20)=160.6\) cm.

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