Calculate two normal tail probabilities.

Calculate two normal tail probabilities.

6 marks
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The heights of a group of students are normally distributed with a mean of 160 cm and a standard deviation of 20 cm.

  1. A student is chosen at random. Find the probability that the student’s height is greater than 180 cm.
  2. In this group of students, 11.9% have heights less than d cm. Find the value of d.

[6]

Solution:

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Answer:For the 11.9th percentile, \(z\approx-1.18\), so \(d=160+20(-1.18)=136.4\) cm.

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