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Statistics - BTM8104-Wk3
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Normal Distribution and Probability Theory

Rudimentary probability theory is the primary focus of this section. Since many everyday situations are based on probabilistic reasoning and occurrences, it is important to have an understanding of probability theory and its connection to statistics. For example, choosing a life insurance policy is a decision that is influenced heavily by probability theory. Studying this fundamental statistical concept will not only support your scholarly academic goals, but will also help you to understand how probability influences decisions in your everyday life.

This section also examines the important statistical concept of the normal probability distribution. Many forms of data analysis utilize this concept, and many elements in our daily lives can be extrapolated from the normal probability distribution. In particular, the 68-95-99.7 percent rule, and the central limit theorem will be introduced, along with standard deviation and how it relates to the normal probability distribution.

Additional important concepts found in this section include: normal distribution and area covered, percentiles, standard scores, central limit theorem, understanding statistical significance, expressing and calculating basic probability, law of large numbers, and the gamblers fallacy.

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Statistics - BTM8104-Wk3
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Chapter Five       If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours? z =       Data Value – Mean             Standard Deviation             2500 – 2500 = 0                         500 Using Excel - NORMSDIST(0) = 0.50 or 50%   The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side? Using the 68-95-99.7 Rule Precisely 68.3 % of light bulbs lie within 1 standard deviation of the mean that will equate to 34.1% on either side   The amount of Jen’s monthly phone bill is normally distributed with a mean of \$60 and a standard deviation of \$12.  Fill in the blanks: 68% of her phone bills are between \$______________ and \$______________.                         Using the 68-95-99.7 Rule                         Using 60 as the mean and 12 as the deviation we get                         60 + 12 = 72                         60 – 12 = 48                         Therefore 68% of Jen’s phone bill falls between \$48 and \$72   The amount of Jen’s monthly phone bill is normally distributed with a mean of \$50 and a standard deviation of \$10.  Find the 25th percentile. z =       Data Value – Mean Standard Deviation and z table value for 25th Percentile -0.674 ("Appendix z-score percentile")             -0.674 = x - 50                                                      10                                     Used Excel =SUM(50-0.674*10) = 43.26                                     The 25th Percentile for her bill is \$43.26   The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches.  What percentage of bolts will have a diameter greater than 0.32 inches? Difference between the diameter = 0.32 – 0.30 = 0.02 Standard deviation = 2 ...
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