Chapter 12 – Probability and Statistics12.7 – The Normal Distribution

12.7 – The Normal Distribution• Today we will learn how to:• Determine whether a set of data appears to be normally

distributed or skewed

• Solve problems involving normally distributed data

12.7 – The Normal Distribution• Discrete Probability Distributions – finite number of possible

values• Histogram

• Continuous Probability Distribution – outcome can be any value in an interval of real numbers• Represented by curves

• Symmetric• Bell curve• Normal Distribution

12.7 – The Normal Distribution• Skewed Distribution – curve of histogram that is not

symmetric• Positively skewed – high at the left and tails to the right

• Negatively skewed – high at the right and tails to the left

12.7 – The Normal Distribution• Example 1• Determine whether the data {31, 37, 35, 36, 34, 36, 32, 36, 33,

32, 34, 34, 35, 34} appear to be positively skewed, negatively skewed, or normally distributed

12.7 – The Normal Distribution• Using Normal Distributions• Standardized test scores, lengths of newborn babies, useful life

and size of manufactured items, production levels

• The number of data values must be large for the distribution to be approximately normal

12.7 – The Normal Distribution• Normal Distribution•

• The graph is maximized at the mean• The mean, median and mode are about equal

• About 68% of the values are within one standard deviation of the mean• About 95% of the value are within two standard deviations of the mean• About 99% of the values are within three standard deviations of the

mean

12.7 – The Normal Distribution

• Example 2• Students counted the number of candies in 100 small packages.

They found that the number of candies per package was normally distributed, with a mean of 23 candies per package and a standard deviation of 1 piece of candy.• About how many packages had between 22 and 24 candies?

• What is the probability that a package selected at random had more than 25 candies?

12.6 – Statistical Measures

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