Applications of Normal Curve

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Applications of Normal Curve
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Steps for word problems

• 1. Read the problem carefully.
• 2. Identify values that are given.
• x, m, s, areas
• Draw a diagram, showing given values and shading
  the region.
• Determine what you are asked to find.
• Write a formula and then solve the problem.

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Formula to find area

• 1. Recall from earlier work
• Z (x m) / s
• 2. Look up areas from the tables for the given z
  and shaded region

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Example 1

• It is known that the SAT is normally distributed
  with a mean of 1000 and a standard deviation of
  200.
• What is the probability that a student, selected
  at random, will have a score higher than 1300?

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Example 2

• On a nursing exam, the mean is 79 and the
  standard deviation is 9. What is the probability
  that a student will get lower than 85, assuming
  the scores are normally distributed?

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Example 3

• Express Courier Service has found that the
  delivery times for packages is normally
  distributed, with a mean of 14 hours and a
  standard deviation of 2 hours. What is the
  probability that a randomly selected package will
  be delivered in between 12 and 15 hours?

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Finding x

• To find x, given an area
• 1. Obtain z from table, looking up the given
  area
• 2. Formula x m zs

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Example 4

• Applicants to a prestigious school are required
  to have SAT scores at the 90th percentile or
  higher in order to be eligible for admission.
  SAT scores are normally distributed with a mean
  of 1000 and a standard deviation of 200. What
  minimum score must be achieved on the SAT to be
  eligible?

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Example 5

• Future Electronics makes compact disc players.
  Its research department has found that the life
  of the laser beam is normally distributed with a
  mean of 5000 hours and a standard deviation of
  450 hours. How long should the warranty be if
  they want to replace no more than 5 of the
  players, assuming that the laser beam became
  defective?

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Example 6

• On a auto mechanic aptitude test, the mean score
  is 270 points and the standard deviation is 35
  points. Assuming that the scores are normally
  distributed, find the value Q1.