How many things in everyday life can be modeled with a normal distribution.
In this section you learned how many things in everyday life can be modeled with a normal distribution.
All normal curves have two parameters: _____ and __ ___
The center of the curve is determined by the value of _ ___
How wide the curve gets is determined by the value of ____ __
What will happen to the graph of a normal curve if we increase the value of μ?
What will happen to the graph of a normal curve if we increase the value of σ?
The transition points (inflection points) are the places where the curve changes from a “hill” to a “valley”. The distance from the mean to the transition point is ___, _______ _________________.
The area under the whole curve is exactly ____.
Fill in the 8 areas of the curve below with the correct 8 percentages for a normal curve.
Fill in the following as you work through your given problems in MyOpenMath.
1. μ= _____ because _____mean is the on the axis at the center of the curve is the mean of a normal distribution.
σ= ______ because ___ the distance from the mean to the transition point is 9
2. μ= _____ because _____ mean is the on the axis at the center of the curve is the mean of a normal distribution._________________________________________________
σ= ______ because ________ the distance from the mean to the transition point is 9________________________________________________
3. Compare the means:____ The three distributions have different values for the mean___________________________________________________________
Explain your reasoning:________ because each curve has a different center;
Compare the standard deviations: the three distributions have the same standard deviation
Explain your reasoning:_________ because the distance from each graph’s mean to the transition point or inflection point is the same for each distribution___________________________________________________
4. Compare the means: ____ The three distributions all have the same mean___________________________________________________________
Explain your reasoning: _____ because each curve has the same center_______________________________________________________
__________________________________________________________________________________
Compare the standard deviations: ____ the three distributions have different standard deviations___________________________________________________
Explain your reasoning: ___ because the distance from each graph’s mean to the transition point or inflection point is different for each distribution_________________________________________________________
5.a. Individual: a randomly selected __dishwasher__________________________________
Variable: _____________lifetime_______________________
Type of variable: qualitative quantitative-discrete quantitative-continuous
b. rv X = the _______ lifetime _________________________________________of a r.s. ___________ dishwasher ______
List the given values with their correct symbols: μ ____ = __________ __ ___ = ___________
c. The Empirical Rule can be used because __ approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. ______________________________________________
Fill in the following with the correct 8 percentages and correct 7 values on the axis.
d. P( 5.25< X ?<18.75 ) = ___________________________ = ___________
Interpret in the context of this problem:
_________________There is about 99.7% of dishwashers that last between 5.25 years and 18.75 years.________________________________________________________
e. P( X ?≥5.25 ) = __________0.15_________________ = __0.15%_________
6.a. Individual: ________________________________
Variable: ____________ ________________________
Type of variable:
b.rv X = the _____________ ___________________________________ of a r.s. ________ _________
List the given values with their correct symbols: _ μ ___ = __________ __ σ ___ = ___________
c. The Empirical Rule can be used because __it is used to approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. ______________________________________________
Fill in the following with the correct 8 percentages and correct 7 values on the axis.
d. P( 397<( X) ?<865 ) = ___________________________ = __________
Interpret in the context of this problem:
e. P( ( X) ?≥631 ) = ___________________________ = ___________
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