Normal Distribution

A normal distribution is a continuous probability distribution that is symmetrical around the mean.
It is defined by two parameters:
  * μ– the mean (average),
  * σ– the standard deviation.

The total area under the curve is equal to 1.
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Example 1: Heights

The heights of adult men are normally distributed with a mean of μ=175 cm and a standard deviation
σ=8 cm.

What is the probability that a randomly selected man is:
  + a) Shorter than 180 cm?
  + b) Taller than 190 cm?
  + c) Between 170 cm and 185 cm?
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Example 2: Exam Scores

The results of a standardized math exam are normally distributed with:
  * μ=70
  * σ=10

Let X be the score of a randomly selected student.

What percentage of students scored:
  + a) More than 85?
  + b) Less than 60?
  + c) Between 65 and 90?
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Reverse problem

The weights of apples are normally distributed with mean 150 g and standard deviation 12 g.

What weight corresponds to the top 10% of heaviest apples?

(Hint: Use the z-score for the 90th percentile.)
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