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Unformatted text preview: MGT 2250 — Lesson 18
Continuous Probability Distributions:
The Standard Normal Distribution
March 7, 2011 Deﬁnition: The standard normal distribution has a mean of “zero” and a standard deviation of “one”.
Any normal distribution can be converted to the standard normal distribution
(standardized) and then the standard normal distribution is used to determine probabilities.
This is done by converting the raw values of any normal distribution to “zscores”. A table is then used to determine probabilities based on umbers of standard
deviations from the mean. z—scores and the Table. ,2 V2 2:: WW « a: EM :3 :M w“ “W’ V {re s n «{4} law
an Example # 1: It has been determined that the mean weight of dogs is pounds with
a standard deviation 0112 pounds. a.) What is the probability a dog ill weigh less than 15 pounds? 5/ f ﬁméwwcj'j «LA/i M (53 Egg: b.) What is the probability a dog will weigh more than 68 pounds? c.) What is the probability a dog will weigh between 34 and 48 pounds? (1.) What is the probability a dog will weigh between 42 and 46 pounds? e.) What is the probability a dog will weigh more than 80 pounds? f.) A dog is categorized as “extremely large” if it is the upper 5% of dogs
in body weight. How many pounds must the weight of a dog exceed
for it to be in the “extremely large” category? «««« hm "mix Example # 2: Everlast ear batteries have been determined to have a mean useful life
of 60 months with a standard deviation of 12» months. i i y, a f";
' g
i g 3‘“ J u
i W, a, ., ._ if
i
E at) What is the probability a liattery will last more than 72 months? b.) What is the probability a battery will last less than 54 months? c.) What is the probability battery will last between 56 and 68 months? d.) What is the probability battery will last between 62 and 74 months? e.) Everlast offers a free replacement battery to any customer whose
battery does not last as long as the minimum lifetime guaranteed. In
establishing that guarantee period, the company did not want to have
to replace more than 1% of their batteries. What is the minimum
lifetime in months the company should guarantee for its batteries in
order to have a 1% probability or less of replacing a battery? ____ , “MW “MK \KNL ‘F,Www ...
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This note was uploaded on 02/05/2012 for the course MGT 2250 taught by Professor Milne during the Summer '08 term at Georgia Institute of Technology.
 Summer '08
 Milne

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